116. |
Julian Lenz, Michael Mandl and Andreas Wipf
|
|
Magnetized (2+1)-dimensional Gross-Neveu model at finite density
|
|
We perform a lattice study of the (2+1)-dimensional Gross-Neveu model in a background
magnetic field B and at non-zero chemical potential μ. The complex-action problem arising in our simulations using overlap fermions is under control. For B=0
we observe a first-order phase transition in μ even at non-vanishing
temperatures. Our main finding, however, is that
the rich phase structure found in the limit of infinite flavor number N
is washed out by
the fluctuations present at Nf=1. We find no evidence for inverse magnetic catalysis, i.e.,
the decrease of the order parameter of chiral symmetry breaking with B
for μ close to the chiral phase transition. Instead, the magnetic field
tends to enhance the breakdown of chiral symmetry for all values of μ below
the transition. Moreover, we find no trace of spatial inhomogeneities
in the order parameter. We briefly comment on the potential relevance of our
results for QCD.
|
| Phys. Rev. D108 (2023) 074508 |
| pdf file (570 KB) |
| |
| |
| |
115. |
Julian Lenz, Michael Mandl and Andreas Wipf
|
|
Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model
|
|
We study the Gross-Neveu model in 2+1 dimensions in an external magnetic field B. We
first summarize known mean-field results, obtained in the limit of large flavor number N,
before presenting lattice results using the overlap discretization to study one reducible
fermion flavor, N=1. Our findings indicate that the magnetic catalysis phenomenon, i.e.,
an increase of the chiral condensate with the magnetic field, persists beyond the mean-field
limit for temperatures below the chiral phase transition and that the critical
temperature grows with increasing magnetic field. This is in contrast to the situation in QCD, where the
broken phase shrinks with increasing B while the condensate exhibits a
non-monotonic B-dependence close to the chiral crossover, and we comment on this discrepancy. We do not find
any trace of inhomogeneous phases induced by the magnetic field.
|
| Phys. Rev. D107 (2023) 094505 |
| pdf file (680 KB) |
| |
| |
| |
114. |
Andreas Wipf und Julian Lenz
|
|
Symmetries of Thirring models on 3d Lattices
|
|
We review some recent developments
about strongly interacting relativistic Fermi theories
in three spacetime dimensions. These models realize the
asymptotic safety scenario and are used to describe
the low-energy properties of Dirac materials in condensed
matter physics. We begin with a general discussion
of the symmetries of multi-flavor Fermi systems
in arbitrary dimensions.
Then we review known results about the critical flavor
number Ncrit of Thirring
models in three dimensions. Only models with flavor number below
Ncrit show a phase transition from a symmetry-broken
strong-coupling phase to a symmetric weak-coupling phase.
Recent simulations with chiral fermions
show that critis smaller than previously
extracted with various non-perturbative methods. Our simulations
with chiral SLAC fermions reveal that
for four-component flavors Ncrit=0.80(4).
This means that all reducible Thirring models with Nr=1,2,3,...
show no phase transition with order parameter.
Instead we discover footprints of phase transitions without order
parameter. These new transitions are probably smooth
and could be used to relate the lattice Thirring models to
Thirring models in the continuum. For a single irreducible
flavor, we provide previously unpublished values for the
critical couplings and critical exponents.
|
| Symmetry 14 (2022) 333 |
| pdf file (1681 KB) |
| |
| |
| |
113. |
Julian Lenz, Michael Mandl and Andreas Wipf
|
|
Inhomogeneities in the 2-Flavor Chiral Gross-Neveu Model
|
|
We investigate the finite-temperature and -density
chiral Gross-Neveu model with an axial UA(1) symmetry
in 1+1 dimensions on the lattice. In the limit where the number of
flavors N tends to infinity the continuum model has been solved
analytically and shows two phases: a symmetric
high-temperature phase with a vanishing condensate and a low-temperature
phase in which the complex condensate forms a chiral spiral which
breaks translation invariance.
In the lattice simulations we employ
chiral SLAC fermions with exact axial symmetry.
Similarly to N→∞, we find for 8 flavors,
where quantum and thermal fluctuations are suppressed, two distinct regimes in the
(T,μ) phase diagram, characterized by qualitatively different behavior
of the two-point functions of the condensate fields. More surprisingly,
at N=2, where fluctuations are no longer suppressed, the model still
behaves similarly to the N→∞ model and we conclude that the chiral
spiral leaves its footprints even on systems with a small number of flavors.
For example, at low temperature
the two-point functions are still dominated by chiral spirals with pitches proportional to the inverse chemical potential,
although in contrast to large-$\Nf$ their amplitudes decrease with distance. We argue that these results should not be interpreted as the spontaneous breaking of a continuous symmetry, which is forbidden in two dimensions. Finally, using Dyson-Schwinger
equations we calculate the decay
of the UA(1)-invariant fermion four-point function
in search for a BKT phase at zero temperature.
|
| Phys. Rev. D105 (2022) 034512 |
| pdf file (2070 KB) |
| |
| |
| |
112. |
Marc Steinhauser, Andre Sternbeck, Börn Wellegehausen and Andreas Wipf
|
|
N=1 Super-Yang-Mills theory on the lattice with twisted mass fermions
|
|
Super-Yang-Mills theory (SYM)
is a central building block for supersymmetric extensions
of the Standard Model of particle physics. Whereas the weakly coupled
subsector of the latter can be treated within a perturbative setting,
the strongly coupled subsector must be dealt with a non-perturbative
approach. Such an approach is provided by the lattice formulation.
Unfortunately a lattice regularization breaks supersymmetry and consequently
the mass degeneracy within a supermultiplet. In this article
we investigate the properties of N=1 SYM with lattice Wilson Dirac operator
with an additional parity mass, similar as in twisted mass lattice QCD.
We show that a special 45° twist effectively removes the mass splitting of the
chiral partners. Thus, at finite lattice spacing both chiral and supersymmetry
are enhanced resulting in an improved continuum extrapolation.
Furthermore, we show that for the non-interacting theory at 45°
twist discretization errors of order O(a) are suppressed,
suggesting that the same happens for the interacting theory as well.
As an aside, we demonstrate that the DDαAMG multigrid
algorithm accelerates the
inversion of the Wilson Dirac operator considerably.
On a 16×16×16×32,
lattice speed-up factors
of up to 20 are reached if commonly used algorithms are replaced by the DDαAMG.
|
| JHEP 01 (2021) 154 |
| pdf file (1243 KB) |
| |
| |
| |
111. |
Julian Lenz, Laurin Pannullo, Marc Wagner, Börn Wellegehausen and Andreas Wipf
|
|
Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
|
|
In a recent work we studied the phase structure of the
Gross-Neveu (GN) model in 1+1 dimensions at finite number of fermion flavors
Nf = 2, 8, 16, finite temperature and finite chemical potential using lattice field theory. Most importantly, we found an inhomogeneous phase at low temperature and large chemical potential, quite similar to the analytically solvable Nf → ∞ limit.
In the present work we continue our lattice field theory investigation of the
finite-Nf GN model by studying the formation of baryons, their spatial distribution and their relation to the chiral condensate. As a preparatory step we also discuss a linear coupling of lattice fermions to the chemical potential.
|
| Phys. Rev. D102 (2020) 114501 |
| pdf file (771 KB) |
| |
| |
| |
110. |
Julian Lenz, Laurin Pannullo, Marc Wagner, Börn Wellegehausen and Andreas Wipf
|
|
Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions
|
|
We explore the thermodynamics of the 1+1-dimensional Gross-Neveu (GN) model at
finite number of fermion flavors Nf, finite temperature and
finite chemical potential using lattice field theory. In the limit
Nf → ∞ the model has been solved analytically in the
continuum. In this limit three phases exist: a massive phase, in which a
homogeneous chiral condensate breaks chiral symmetry spontaneously, a
massless symmetric phase with vanishing condensate and most interestingly
an inhomogeneous phase with a condensate, which oscillates in the spatial
direction. In the present work we use chiral lattice fermions
(naive fermions and SLAC fermions) to simulate the GN model
with 2, 8 and 16 flavors. The results obtained with both discretizations
are in agreement. Similarly as for Nf → ∞ we find
three distinct regimes in the phase diagram, characterized by a qualitatively
different behavior of the two-point function of the condensate field.
For Nf = 8 we map out the phase diagram in detail and obtain
an inhomogeneous region smaller as in the limit Nf → ∞,
where quantum fluctuations are suppressed. We also comment on the existence
or absence of Goldstone bosons related to the breaking of translation
invariance in 1+1 dimensions.
|
| Phys. Rev. D101 (2020) 094512 |
| pdf file (2634 KB) |
| |
| |
| |
109. |
Luis Inzunza, Mikhail S. Plyushchay and Andreas Wipf
|
|
Hidden symmetry and (super)conformal mechanics in a monopole background
|
|
We study classical and quantum hidden symmetries of a particle with electric charge e
in the background of a Dirac monopole of magnetic charge g subjected
to an additional central potential V(r)=U(r) +(eg)2/2mr2
with U(r)=mω2r2/2, similar to that in the
one-dimensional conformal mechanics model of de Alfaro, Fubini and Furlan (AFF).
By means of a non-unitary conformal bridge transformation,
we establish a relation of the quantum states and of all symmetries of the system
with those of the system without harmonic trap, U(r)=0.
Introducing spin degrees of freedom via a very special spin-orbit
coupling, we construct the osp(2.2) superconformal extension
of the system with unbroken N=2 Poincaré supersymmetry
and show that two different superconformal extensions of the one-dimensional AFF
model with unbroken and spontaneously broken supersymmetry have a common origin.
We also show a universal relationship between the dynamics of a Euclidean particle
in an arbitrary central potential U(r) and the dynamics of a charged particle
in a monopole background subjected to the potential V(r).
|
| JHEP 04 (2020) 028 |
| pdf file (3265 KB) |
| |
| |
| |
108. |
Luis Inzunza, Mikhail S. Plyushchay and Andreas Wipf
|
|
Conformal bridge between freedom and confinement
|
|
We construct a non-unitary transformation that relates a given "asymptotically free"
conformal quantum mechanical system Hf with its confined, harmonically
trapped version Hc. In our construction, Jordan states corresponding
to the zero eigenvalue of Hf, as well as its eigenstates and Gaussian
packets are mapped into the eigenstates, coherent states and squeezed states of
Hc, respectively. The transformation is an automorphism of the
conformal sl(2,R) algebra of the nature of the fourth-order root of the
identity transformation, to which a complex canonical transformation corresponds
on the classical level being the fourth-order root of the spatial reflection.
We investigate the one- and two-dimensional examples which reveal, in particular,
a curious relation between the 2D free particle and the Landau problem.
|
| Phys. Rev. D101 (2020) 105019
|
| pdf file (378 KB) |
| |
| |
| |
107. |
Julian J. Lenz, Andreas Wipf, Bjoern H. Wellegehausen
|
|
Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions
|
|
The Thirring model is an interacting fermion theory with
current-current interaction.
The model in 1+2 dimensions
has applications in condensed-matter physics to describe the
electronic excitations of Dirac materials.
Earlier investigations with Schwinger-Dyson equations,
the functional
renormalization group and lattice simulations with staggered fermions suggest that a critical number of (reducible)
flavors Nc exists, below which chiral symmetry can be
broken spontaneously. Values for
Nc found in the literature
vary between 2 and 7.
Recent lattice studies with chirally invariant SLAC
fermions have indicated that chiral symmetry is unbroken for
all integer flavor numbers.
An independent simulation based on domain wall fermions
seems to favor a critical flavor-number
that satisfies 1<Nc<2. However,
in the latter simulations difficulties in reaching
the massless limit in the broken phase
(at strong coupling and after the Ls → ∞ limit
has been taken) are encountered. To find an accurate
value Nc we study the Thirring model
(by using an analytic continuation of the parity
even theory to arbitrary real N) for N
between 0.5 and 1.1. We investigate the
chiral condensate, the spectral
density of the Dirac operator, the spectrum
of (would-be) Goldstone bosons and
the variation of the filling-factor and
conclude that the critical
flavor number is Nc=0.80(4).
Thus we see no
chiral symmetry breaking in all Thirring models with
1 or more flavors of (4-component) fermions.
Besides the artifact transition to the
unphysical lattice artifact phase we find
strong evidence for a hitherto unknown phase
transition that exists for N>Nc
and should answer the question of where to
construct a continuum limit.
|
| Phys. Rev. D100 (2019) 054501 |
| pdf file (761 KB) |
| |
| |
| |
106. |
Daniel August, Marc Steinhauser, Bjoern Wellegehausen and Andreas Wipf
|
|
Mass spectrum of 2-dimensional N=(2,2) super Yang-Mills theory on the lattice
|
|
In the present work we analyse N=(2,2) supersymmetric Yang-Mills
(SYM) theory
in two dimensions by means of lattice simulations. The theory arises as
dimensional reduction of N=1 SYM theory
in four dimensions.
As in other gauge theories with extended supersymmetry,
the classical scalar potential has flat directions which
may destabilize numerical simulations. In addition,
the fermion determinant need not be positive and this sign-problem
may cause further problems in a stochastic treatment.
We demonstrate that N=(2,2) super Yang-Mills theory
has actually no sign problem and that the flat directions are
lifted and thus stabilized by quantum corrections. Only the
bare mass of the scalars experience a finite additive renormalization
in this finite theory. On various lattices with different lattice constants
we determine the scalar masses and hopping parameters for which
the supersymmetry violating terms are minimal. By studying four
Ward identities and by monitoring the $\pi$-mass we show that
supersymmetry is indeed restored in the continuum limit. In the second part
we calculate the masses of the low-lying bound states. We find that
in the infinite-volume and supersymmetric continuum limit the
Veneziano-Yankielowicz super-multiplet becomes massless and the
Farrar-Gabadadze-Schwetz super-multiplet decouples from the theory.
In addition, we estimate the masses of the excited mesons in the
Veneziano-Yankielowicz multiplet. We observe that the gluino-glueballs
have comparable masses to the excited mesons.
|
| JHEP 1901 (2019) 099 |
| pdf file (1795 KB) |
| |
| |
| |
105. |
Polina Feldmann, Andreas Wipf and Luca Zambelli
|
|
Critical Wess-Zumino models with four supercharges from the functional renormalization group
|
|
We analyze the N=1 supersymmetric Wess-Zumino model
dimensionally reduced to the N= supersymmetric model
in three Euclidean dimensions. As in the original model in four dimensions
and the N=(2,2) model in two dimensions the
superpotential is not renormalized. This property puts severe
constraints on the non-trivial fixed-point solutions,
which are studied in detail.
We admit a field-dependent wave function renormalization that
in a geometric language relates to a Kähler metric.
The Kähler metric is not protected by supersymmetry and
we calculate its explicit form at the fixed point.
In addition we determine the exact quantum dimension of the
chiral superfield and several critical
exponents of interest, including the correction-to-scaling exponent
ω, within the functional renormalization group approach.
We compare the results obtained at different levels of
truncation, exploring also a momentum-dependent wave function renormalization.
Finally we briefly describe a tower of multicritical models in continuous dimensions.
|
| Phys. Rev. D98 (2018) 096005 |
| pdf file (496 KB) |
| |
| |
| |
104. |
Boris Merzlikin, Ilya Shapiro, Andreas Wipf and Omar Zanusso
|
|
Renormalization group flows and fixed points
for a scalar field in curved space
with nonminimal F(φ)R coupling
|
|
Using covariant methods, we construct and explore the Wetterich
equation for a non-minimal coupling F(φ)R of a
quantized scalar field to the Ricci scalar of a prescribed curved space.
This includes the often considered non-minimal coupling
ξRφ2 as a special case. We consider the
truncations without and with scale- and field-dependent
wave function renormalization in dimensions between four and two.
Thereby the main emphasis is on analytic and numerical solutions of the
fixed point equations and the behavior in the vicinity
of the corresponding fixed points. We determine the non-minimal
coupling in the symmetric and spontaneously broken phases
with vanishing and non-vanishing average fields, respectively.
Using functional perturbative renormalization group methods,
we discuss the leading universal contributions to the RG flow
below the upper critical dimension d=4.
|
| Phys. Rev. D96 (2017) 125007 |
| pdf file (440 KB) |
| |
| |
| |
103. |
Bjoern Wellegehausen, Daniel Schmidt and Andreas Wipf
|
|
Critical flavour number of the Thirring model in three dimensions
|
|
The Thirring model is a four-fermion theory with a current-current interaction and U(2N) chiral symmetry.
It is closely related to three-dimensional QED and other models used to describe properties of graphene.
In addition it serves as a toy model to study chiral symmetry breaking.
In the limit of flavour number N → 1/2 it is equivalent to the Gross-Neveu model, which shows a parity-breaking discrete phase transition.
The model was already studied with different methods, including Dyson-Schwinger
equations, functional renormalisation group methods and lattice
simulations.
Most studies agree that there is a phase transition from a symmetric phase to a spontaneously broken phase for a small number of fermion flavours, but no symmetry breaking for large N.
But there is no consensus on the critical flavour number Ncrit
above which there is no phase transition anymore and on
further details of the critical behaviour.
Values of N found in the literature vary between 2 and 7.
All earlier lattice studies were performed with staggered fermions. Thus it is questionable if in the continuum limit the lattice model recovers the internal symmetries of the continuum model.
We present new results from lattice Monte Carlo simulations of the Thirring model
with SLAC fermions which exactly implement all internal
symmetries of the continuum model
even at finite lattice spacing.
If we reformulate the model in an irreducible representation of the Clifford algebra, we find, in contradiction to earlier results, that the behaviour for even and odd flavour numbers is very different:
For even flavour numbers, chiral and parity symmetry are always unbroken.
For odd flavour numbers parity symmetry is spontaneously broken below the critical flavour number Nir,crit=9 while chiral symmetry is still unbroken.
|
| Phys. Rev. D96 (2017) 094504 (Editor's choice) |
| pdf file (525 KB) |
| |
| |
| |
102. |
Holger Gies, Tobias Hellwig, Andreas Wipf and Omar Zanusso
|
|
A functional perspective on emergent supersymmetry
|
|
We investigate the emergence of N=1 supersymmetry in the long-range behavior
of three-dimensional parity-symmetric Yukawa systems.
We discuss a renormalization approach that manifestly preserves supersymmetry
whenever such symmetry is realized,
and use it to prove that supersymmetry-breaking operators are irrelevant,
thus proving that such operators are suppressed in the infrared.
All our findings are illustrated with the aid of the ε-expansion and a functional variant of perturbation theory,
but we provide numerical estimates of critical exponents that are based on the non-perturbative functional renormalization group.
|
| JHEP 1712 (2017) 132 |
| pdf file (347 KB) |
| |
| |
| |
101. |
Tobias Hellwig, Andreas Wipf and Omar Zanusso
|
|
Scaling and superscaling solutions from the functional renormalization group
|
|
We study the renormalization group flow of Z2-invariant
supersymmetric and non-supersymmetric scalar models
in the local potential approximation using functional renormalization group methods.
We focus our attention to the fixed points of the renormalization group flow of these models,
which emerge as scaling solutions.
In two dimensions these solutions are interpreted as the minimal (supersymmetric) models of conformal field theory,
while in three dimension they are manifestations of the Wilson-Fisher universality class and its supersymmetric counterpart. We also study the analytically continued
flow in fractal dimensions between 2 and 4 and determine the critical dimensions
for which irrelevant operators become relevant and change the universality
class of the scaling solution.
We also include novel analytic and numerical investigations of the properties that determine the occurrence of the scaling solutions within the method.
For each solution we offer new techniques to compute the spectrum of the deformations
and obtain the corresponding critical exponents.
|
| Phys. Rev. D92 (2015) 085027 |
| pdf file (1036 KB) |
| |
| |
| |
100. |
Ilya Shapiro, Poliane de Morais Teixeira and Andreas Wipf
|
|
On the functional renormalization group for the scalar file on
curved background with non-minimal interaction. |
|
The running of the non-minimal parameter ξ of
the interaction of the real scalar field and scalar curvature
is explored within the non-perturbative setting of the func-
tional renormalization group (RG). We establish the RG flow
in curved space-time in the scalar field sector, in particular
derive an equation for the non-minimal parameter. The RG
trajectory is numerically explored for different sets of initial
data.
|
| Eur. Phys. J. C 75 C (2015) 262 |
| pdf file (468 KB) |
| |
| |
| |
99. |
Marianne Heilmann, Tobian Hellwig, Benjamin Knorr, Marcus Ansorg and Andreas Wipf
|
|
Convergence of Derivative Expansion in Supersymmetric Functional RG Flows. |
|
We confirm the convergence of the derivative expansion in two supersymmetric models via the functional
renormalization group method. Using pseudo-spectral methods, high-accuracy results for the lowest
energies in supersymmetric quantum mechanics and a detailed description of the supersymmetric
analogue of the Wilson-Fisher fixed point of the three-dimensional Wess-Zumino model are obtained.
The superscaling relation proposed earlier, relating the relevant critical exponent to the anomalous
dimension, is shown to be valid to all orders in the supercovariant derivative expansion and for all d≥2.
|
| JHEP 1502 (2015) 109 |
| pdf file (1430 KB) |
| |
| |
| |
98. |
Björn Wellegehausen, Daniel Körner and Andreas Wipf
|
|
Asymptotic safety on the lattice: The Nonlinear O(N) Sigma Model. |
|
We study the non-perturbative renormalization group flow of the nonlinear O(N) sigma model in
two and three spacetime dimensions using a scheme that combines an effective local Hybrid Monte
Carlo update routine, blockspin transformations and a Monte Carlo demon method. In two dimensions
our results verify perturbative renormalizability. In three dimensions, we determine the flow diagram
of the theory for various N and different truncations and find a non-trivial fixed point, which
indicates non-perturbative renormalizability. It is related to the well-studied phase transition
of the O(N) universality class and characterizes the continuum physics of the model. We compare
the obtained renormalization group flows with recent investigations by means of the Functional
Renormalization Group.
|
| Annals of Physics 349 (2014) 374 |
| pdf file (575 KB) |
| |
| |
| |
97. |
Björn Wellegehausen, Axel Maas, Andreas Wipf and Lorenz von Smekal
|
|
Hadron masses and baryonic scales in G2-QCD at finite density. |
|
The QCD phase diagram at densities relevant to neutron stars remains elusive, mainly due
to the fermion-sign problem. At the same time, a plethora of possible phases has
been predicted in models. Meanwhile G2-QCD, for which the SU(3) gauge group of QCD is
replaced by the exceptional Lie group G2, does not have a sign problem and can
be simulated at such densities using standard lattice techniques.
It thus provides benchmarks to models and functional continuum methods, and it serves to
unravel the nature of possible phases of strongly interacting matter at high densities.
Instrumental in understanding these phases is that G2-QCD has fermionic baryons,
and that it can therefore sustain a baryonic Fermi surface.
Because the baryon spectrum of G2-QCD also contains bosonic diquark and probably other
more exotic states, it is important to understand this spectrum before one can disentangle
the corresponding contributions to the baryon density. Here we present the first
systematic study of this spectrum from lattice simulations at different quark masses.
This allows us to relate the mass hierarchy, ranging from scalar would-be-Goldstone bosons
and intermediate vector bosons to the G2-nucleons and deltas, to individual
structures observed in the total baryon density at finite chemical potential.
|
| Phys. Rev. D89 (2014) 056007 |
| pdf file (233 KB) |
| |
| |
| |
96. |
Mikhail Plyushchay and Andreas Wipf
|
|
Particle in a self-dual dyon background: hidden free nature, and exotic superconformal
symmetry. |
|
We show that a non-relativistic particle in a combined field of a magnetic
monopole and 1/r2 potential reveals a hidden, partially free dynamics when
the strength of the central potential and the charge-monopole coupling constant are
mutually fitted to each other. In this case the system admits both a conserved
Laplace-Runge-Lenz vector and a dynamical conformal symmetry.
The supersymmetrically extended system corresponds then to a background of a
self-dual or anti-self-dual dyon. It is described by a quadratically extended
Lie superalgebra D(2,1;α) with α=1/2, in which the bosonic
set of generators is enlarged by a generalized Laplace-Runge-Lenz vector and
its dynamical integral counterpart related to Galilei symmetry, as well as by the chiral
Z2-grading operator. The odd part of the nonlinear superalgebra comprises
a complete set of 24=2×3×4 fermionic generators.
Here a usual duplication comes from the Z2-grading structure, the second
factor can be associated with a triad of scalar integrals --- the Hamiltonian, the generator
of special conformal transformations and the squared total angular momentum vector,
while the quadruplication is generated by a chiral spin vector integral
which exits due to the (anti)-self-dual nature of the electromagnetic background.
|
| Phys. Rev. D89 (2014) 045017 |
| pdf file (361 KB) |
| |
| |
| |
95. |
Raphael Flore, Andreas Wipf and Omar Zanusso
|
|
Functional renormalization group of the nonlinear sigma model and the O(N)
universality class. |
|
We study the renormalization group flow of the O(N) nonlinear sigma model in
arbitrary dimensions. The effective action of the model is truncated to fourth order
in the derivative expansion and the flow is obtained by combining the
non-perturbative renormalization group and the background field method.
We investigate the flow in three dimensions and analyze the phase structure
for arbitrary N. While a nontrivial fixed point is present in a reduced truncation
of the effective action and has critical properties which can be related to the
well-known features of the O(N) universality class, one of the fourth order operators
destabilizes this fixed point and has to be discussed carefully.
|
| Phys.Rev. D87 (2013) 065019 |
| pdf file (584 KB) |
| |
| |
| |
94. |
Marianne Mastaler, Franziska Synatschke-Czerwonka and Andreas Wipf
|
|
Supersymmetric renormalization group flows. |
|
The functional renormalization group equation for the quantum effective action is a powerful tool to investigate non-perturbative phenomena in quantum field theories. We discuss the application of manifest supersymmetric flow equations to the N = 1 Wess-Zumino model in two and three dimensions and the linear O(N) sigma model in three dimensions in the large-N limit. The former is a toy model for dynamical supersymmetry breaking, the latter for an exactly solvable field theory.
|
| Phys. Part. Nucl. 43 (2012) 593 |
| pdf file (769 KB) |
| |
| |
| |
93. |
Marianne Heilman, Daniel Litim, Franziska Synatschke-Czerwonka and Andreas Wipf
|
|
Phases of supersymmetric O(N) theories. |
|
We perform a global renormalization group study of O(N) symmetric Wess-Zumino theories
and their phases in three euclidean dimensions. At infinite N the theory is solved exactly.
The phases and phase transitions are worked out for finite and infinite short-distance cutoffs.
A distinctive new feature arises at strong coupling, where the effective superfield potential
becomes multi-valued, signalled by divergences in the fermion-boson interaction. Our findings
resolve the long-standing puzzle about the occurrence of degenerate O(N) symmetric phases. At
finite N, we find a strongly-coupled fixed point in the local potential approximation and explain
its impact on the phase transition. We also examine the possibility for a supersymmetric
Bardeen-Moshe-Bander phenomenon, and relate our findings with the spontaneous breaking of supersymmetry
in other models.
|
| Phys. Rev. D86 (2012) 105006 |
| pdf file (6722 KB) |
| |
| |
| |
92. |
Raphael Flore, Daniel Körner, Andreas Wipf and Christian Wozar
|
|
Supersymmetric Nonlinear O(3) Sigma Model on the Lattice.
|
|
A supersymmetric extension of the nonlinear O(3) sigma model in two spacetime dimensions is investigated by means of Monte Carlo simulations. We argue that it is impossible to construct a lattice action that implements both the O(3) symmetry as well as at least one supersymmetry exactly at finite lattice spacing. It is shown by explicit calculations that previously proposed discretizations fail to reproduce the exact symmetries of the target manifold in the continuum limit. We provide an alternative lattice action with exact O(3) symmetry and compare two approaches based on different derivative operators. Using the nonlocal SLAC derivative for the quenched model on moderately sized lattices we extract the value sigma(2,u0) = 1.2604(13) for the step scaling function at
u0 = 1.0595, to be compared with the exact value 1.261210. For the supersymmetric model with SLAC derivative the discrete chiral symmetry is maintained but we encounter strong sign fluctuations, rendering large lattice simulations ineffective.
By applying the Wilson prescription, supersymmetry and chiral symmetry are broken explicitly at finite lattice spacing, though there is clear evidence that both are restored in the continuum limit by fine tuning of a single mass parameter.
|
| JHEP 1211 (2012) 159 |
| pdf file (2075 KB) |
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91. |
Axel Maas, Lorenz von Smekal, Bjoern Wellegehausen and Andreas Wipf
|
|
The phase diagram of a gauge theory with fermionic baryons. |
|
The fermion-sign problem at finite density is a persisting challenge for Monte-Carlo simulations. Theories that do not have a sign problem can provide valuable guidance and insight for physically more relevant ones that do. Replacing the gauge group SU(3) of QCD by the exceptional group G2, for example, leads to such a theory. It has mesons as well as bosonic and fermionic baryons, and shares many features with QCD. This makes the G2 gauge theory ideally suited to study general properties of dense, strongly-interacting matter, including baryonic and nuclear Fermi pressure effects as relevant in compact stars and heavy-ion collisions. We present the first lattice simulations of the phase diagram of this theory at finite temperature and baryon chemical potential.
|
| Phys. Rev. D86 (2012) 111901 |
| pdf file (349 KB) |
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90. |
Kurt Langfeld and Andreas Wipf
|
|
Fermi-Einstein condensation in dense QCD-like theories. |
|
While pure Yang-Mills theory feature the centre symmetry, this symmetry is explicitly
broken by the presence of dynamical matter. We study the impact of the centre symmetry
in such QCD-like theories. In the analytically solvable Schwinger model, centre transitions
take place even under extreme conditions, temperature and/or density, and we show that they
are key to the solution of the Silver-Blaze problem. We then develop an effective SU(3) quark
model which confines quarks by virtue of centre sector transitions. The phase diagram by
confinement is obtained as a function of the temperature and the chemical potential. We show
that at low temperatures and intermediate values for the chemical potential the centre dressed
quarks undergo condensation due to Bose like statistics. This is the Fermi Einstein condensation.
To corroborate the existence of centre sector transitions in gauge theories with matter, we
study (at vanishing chemical potential) the interface tension in the three-dimensional Z2 gauge
theory with Ising matter, the distribution of the Polyakov line in the four-dimensional
SU(2)-Higgs model and devise a new type of order parameter which is designed to detect
centre sector transitions. Our analytical and numerical findings lead us to conjecture
a new state of cold, but dense matter in the hadronic phase for which Fermi Einstein
condensation is realised.
|
| Annals of Physics 327 (2012) 994 |
| pdf file (694 KB) |
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89. |
Christian Wozar and Andreas Wipf
|
|
Supersymmetry Breaking in Low Dimensional Models. |
|
We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions
using lattice methods. Starting from supersymmetric quantum mechanics we explain the fundamental
principles and problems that arise in putting supersymmetric models onto the lattice. We compare
our lattice results (built upon the non-local SLAC derivative) with numerically exact results
obtained within the Hamiltonian approach. A particular emphasis is put on the discussion of
boundary conditions. We investigate the ground state structure, mass spectrum, effective
potential and Ward identities and conclude that lattice methods are suitable to derive the
properties of supersymmetric quantum mechanics, even with broken supersymmetry. Based on
this result we analyse the two dimensional N=1 Wess-Zumino model with spontaneous supersymmetry
breaking. First we show that (in agreement with earlier analytical and numerical studies) the
SLAC derivative is a sensible choice in the quenched model, which is nothing but the two
dimensional φ4 model. Then, we present the very first computation of a renormalised critical
coupling for the complete supersymmetric model. This calculation makes use of Binder cumulants
and is supported by a direct comparison to Ward identity results, both in the continuum and
infinite volume limit. The physical picture is completed by masses at two selected couplings,
one in the supersymmetric phase and one in the supersymmetry broken phase. Signatures of the
Goldstino in the fermionic correlator are clearly visible in the broken case.
|
| Annals of Physics 327 (2012) 774 |
| pdf file (913 KB) |
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88. |
Daniel Litim, Marianne Mastaler, Franzsika Synatschke-Czerwonka and Andreas Wipf
|
|
Critical behavior of supersymmetric O(N) models in the large-N limit. |
|
We derive a supersymmetric renormalization group (RG) equation for the scale-dependent
superpotential of the supersymmetric O(N) model in three dimensions. For a supersymmetric
optimized regulator function, we solve the RG equation for the superpotential exactly in
the large-N limit. The fixed-point solutions are classified by an exactly marginal coupling.
In the weakly coupled regime there exists a unique fixed-point solution, for intermediate
couplings we find two separate fixed-point solutions and in the strong coupling regime no
globally defined fixed-point potentials exist. We determine the exact critical exponents
both for the superpotential and the associated scalar potential. Finally, we relate the
high-temperature limit of the four-dimensional theory to the Wilson-Fisher fixed point
of the purely scalar theory.
|
| Phys. Rev. D 84 125009 (2011) |
| pdf file (1671 KB) |
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87. |
Björn Wellegehausen, Andreas Wipf and Christian Wozar
|
|
Phase diagram of the lattice G2 Higgs Model. |
|
We study the phases and phase transition lines of
the finite temperature G2 Higgs model. Our work
is based on an efficient local hybrid Monte-Carlo algorithm
which allows for accurate measurements of expectation values,
histograms and susceptibilities. On smaller lattices we calculate the
phase diagram in terms of the inverse gauge coupling β and the
hopping parameter κ. For κ > 0 the model reduces to G2 gluodynamics
and for κ → ∞ to SU(3) gluodynamics. In both limits the system
shows a first order confinement-deconfinement transition. We show that
the first order transitions at asymptotic values of the hopping parameter
are almost joined by a line of first order transitions. A careful analysis
reveals that there exists a small gap in the line where the first order
transitions turn into continuous transitions or a cross-over region.
For β → ∞ the gauge degrees of freedom are frozen and one
finds a nonlinear O(7) sigma model which exhibits a second order transition
from a massive O(7)-symmetric to a massless O(6)-symmetric phase. The
corresponding second order line for large β remains second order for
intermediate β until it comes close to the gap between the two first order
lines. Besides this second order line and the first order confinement-deconfinement
transitions we find a line of monopole-driven bulk transitions which do not
interfer with the confinement-deconfinment transitions.
|
| Phys. Rev. D 83 114502 (2011) |
| pdf file (559 KB) |
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86. |
Björn Wellegehausen, Andreas Wipf and Christian Wozar
|
|
Casimir Scaling and String Breaking in G2 Gluodynamics. |
|
We study the potential energy between static charges in
G2 gluodynamics in three and four dimensions. Our work
is based on an efficient local hybrid Monte-Carlo algorithm
and a multi-level Lüscher-Weisz algorithm with exponential
error reduction to accurately measure expectation values
of Wilson and Polyakov loops. Both in three and four
dimensions we show that at intermediate scales the string
tensions for charges in various G2 representations scale with
the second order Casimir. In three dimensions Casimir scaling is
confirmed within four percent for charges in representations
of dimensions 7,14,27,64,77,77',182 and 189
and in four dimensions within five percent
for charges in representations of dimensions 7,14,27 and 64.
In three dimensions we detect string breaking for charges in the
two fundamental representations. The scale for string
breaking agrees very well with the mass of the created pair
of glue-lumps. Close to the string breaking distance Casimir scaling between
adjoint and defining representation is violated by 2.5
percent. The analytical prediction for the continuum string tension
is confirmed for the defining representation in three dimensions.
|
| Phys. Rev. D 83 016001 (2011) |
| pdf file (288 KB) |
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85. |
Franziska Synatschke, Jens Braun and Andreas Wipf
|
|
N=1 Wess Zumino Model in d=3 at zero and finite
temperature. |
|
Supersymmetric renormalization group (RG) flow equations for the effective
superpotential of the three-dimensional Wess-Zumino model are derived
at zero and non-zero temperature. This model with fermions and bosons
interacting via a Yukawa term possesses a supersymmetric analogue of the
Wilson-Fisher fixed-point. At zero temperature we determine the phase-transition
line in coupling-constant space separating the supersymmetric from the
non-supersymmetric phase. At finite temperature
we encounter dimensional reduction from 3 to 2 dimensions
in the infrared regime. We determine the finite-temperature phase diagram
for the restoration of the global Z2-symmetry and
show that for temperatures above the Z2 phase transition the pressure obeys
the Stefan-Boltzmann law of a gas of massless bosons in 2+1 dimensions.
|
| Phys. Rev. D 81 125001 (2010) |
| pdf file (333 KB) |
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84. |
Kurt Langfeld, Bjoern Wellegehausen and Andreas Wipf
|
|
Confinement and the quark Fermi-surface in SU(2N) QCD-like
theories. |
|
Yang-Mills theories with a gauge group SU(Nc≠3) and
quark matter in the fundamental representation share many properties
with the theory of strong interactions, QCD with Nc=3.
We show that, for Nc even and
in the confinement phase, the quark determinant is independent
of the boundary conditions, periodic or anti-periodic ones. We then argue
that a Fermi sphere of quarks can only exist under extreme conditions when
the centre symmetry is spontaneously broken and colour is liberated. Our
findings are supported by lattice gauge simulations for
Nc=2… 5 and are illustrated by means of a simple
quark model.
|
| Phys. Rev. D 81 114502 (2010) |
| pdf file (120 KB) |
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83. |
Franziska Synatschke, Holger Gies and Andreas Wipf
|
|
Phase Diagram and Fixed-Point Structure of two dimensional N=1
Wess-Zumino Model. |
|
We study the phases and fixed-point structure of two-dimensional
supersymmetric Wess-Zumino models with one supercharge. Our work is based on
the functional renormalization group formulated in terms of a manifestly
off-shell supersymmetric flow equation for the effective action. Within the
derivative expansion, we solve the flow of the superpotential also including
the anomalous dimension of the superfield.
The models exhibit a surprisingly rich fixed-point structure with a discrete
number of fixed-point superpotentials. Each fixed-point superpotential is
characterized by its number of nodes and by the number of RG relevant
directions. In limiting cases, we find periodic superpotentials and potentials
which confine the fields to a compact target space. The maximally
IR-attractive fixed point has one relevant direction, the tuning of which
distinguishes between supersymmetric and broken phases. For the Wess-Zumino
model defined near the Gau\ss ian fixed point, we determine the phase diagram
and compute the corresponding ground-state masses.
|
| Phys. Rev. D 80 085007 (2009) |
| pdf file (478 KB) |
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82. |
Bjoern Wellegehausen, Christian Wozar and Andreas Wipf
|
|
Effective Polyakov Loop Dynamics for Finite Temperature G2 Gluodynamics. |
|
Based on the strong coupling expansion we obtain effective
3-dimensional models for the Polyakov loop in finite temperature G2
gluodynamics. The Svetitsky-Jaffe conjecture relates the resulting
continuous spin models with G2 gluodynamics
near phase transition points.
In the present work we analyse the effective theory in leading
order with the help of a generalised mean field approximation and
with detailed Monte Carlo simulations. In addition we derive a
Potts-type discrete spin model by restricting the characters of the
Polyakov loops to the three extremal points of the fundamental
domain of G2. Both the continuous and discrete effective models
show a rich phase structure with a ferromagnetic, symmetric and several
anti-ferromagnetic phases. The phase diagram contains first and second
order transition lines and tricritical points. The modified mean field
predictions compare very well with the results of our simulations.
|
| Phys. Rev. D 80 065028 (2009) |
| pdf file (1009 KB) |
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81. |
Holger Gies, Franziska Synatschke and Andreas Wipf
|
|
Supersymmetry breaking as a quantum phase transition. |
|
We explore supersymmetry breaking in the light of a rich fixed-point
structure of two-dimensional supersymmetric Wess-Zumino models with one
supercharge using the functional renormalization group (RG). We relate the
dynamical breaking of supersymmetry to an RG relevant control parameter of the
superpotential which is a common relevant direction of all fixed points of the
system. Supersymmetry breaking can thus be understood as a quantum phase
transition analogously to similar transitions in correlated fermion
systems. Supersymmetry gives rise to a new superscaling relation between the
critical exponent associated with the control parameter and the anomalous
dimension of the field -- a scaling relation which is not known in standard
spin systems.
|
| Phys. Rev. D 80 101701 (2009) |
| pdf file (120 KB) |
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80. |
Vladimir Kassandrov, Nina Markova, Gerhard Schäfer and Andreas Wipf
|
|
On a model of a classical relativistic particle
of constant and universal mass and spin. |
|
The deformation of the classical action for a point-like particle
recently suggested by A. Staruszkiewicz
gives rise to a spin structure which constrains the values of the
invariant mass and the invariant spin
to be the same for any solution of the equations of motion.
Both these Casimir invariants, the square of the four-momentum vector
and the square of the Pauli-Lubanski vector, are shown to preserve
the same fixed values also in the presence of an arbitrary external electromagnetic field. In the "free" case, in the centre-of-mass
reference frame, the particle moves along a circle of fixed radius
with arbitrary varying frequency. In a homogeneous magnetic field,
a number of rotational "states" is possible with frequencies
slightly different from the cyclotron frequency, and "phase-like"
transitions with spin flops occure at some critical value
of the particle's three-momentum.
|
| J. Phys. A: Math. Theor. 42 315204 (2009) |
| pdf file (213 KB) |
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79. | Wieland Brendel, Falk Bruckmann, Lukas Janssen, Andreas Wipf
and Christian Wozar |
|
Instanton constituents and fermionic zero modes in twisted CP(n) models. |
|
We construct twisted instanton solutions of CP(n) models. Generically a charge-k instanton splits into k(n+1) well-separated and almost static constituents carrying fractional topological charges and being ordered along the noncompact direction. The locations, sizes and charges of the constituents are related to the moduli parameters of the instantons. We sketch how solutions with fractional total charge can be obtained. We also calculate the fermionic zero modes with quasi-periodic boundary conditions in the background of twisted instantons for minimally and supersymmetrically coupled fermions. The zero modes are tracers for the constituents and show a characteristic hopping. The analytical findings are compared to results extracted from Monte-Carlo generated and cooled configurations of the corresponding lattice models. Analytical and numerical results are in full agreement and it is demonstrated that the fermionic zero modes are excellent filters for constituents hidden in fluctuating lattice
configurations.
|
| Phys. Lett. B 676 116-125 (2009) |
| pdf file (766 KB) |
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78. | Franziska Synatschke, Georg Bergner, Holger Gies, Andreas Wipf |
|
Flow Equation for Supersymmetric Quantum Mechanics. |
|
We study supersymmetric quantum mechanics with the functional RG formulated in terms of an exact and manifestly off-shell supersymmetric flow equation for the effective action. We solve the flow equation nonperturbatively in a systematic super-covariant derivative expansion and concentrate on systems with unbroken supersymmetry. Already at next-to-leading order, the energy of the first excited state for convex potentials is accurately determined within a 1% error for a wide range of couplings including deeply nonperturbative regimes.
|
| JHEP 03 028 (2009) |
| pdf file (362 KB) |
| |
| |
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77. | Tobias Kaestner, Georg Bergner, Sebastian Uhlmann,
Andreas Wipf and Christan Wozar |
|
Two-Dimensional Wess-Zumino Models at Intermediate Couplings. |
|
We consider the two-dimensional N=(2,2) Wess-Zumino model with
a cubic superpotential at weak and intermediate couplings.
Refined algorithms allow for the extraction of reliable masses in
a region where perturbation theory no longer applies. We
scrutinize the Nicolai improvement program which is supposed
to guarantee lattice supersymmetry and compare the results for ordinary
and non-standard Wilson fermions with those for SLAC derivatives. It
turns out that this improvement completely fails to enhance simulations
for Wilson fermions and only leads to better results for SLAC fermions.
Furthermore, even without improvement terms the models with all three
fermion species reproduce the correct values for the fermion masses
in the continuum limit.
|
| Phys. Rev. D 78 095001 (2008) |
| pdf file (2200 KB) |
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76. | Franziska Synatschke, Andreas Wipf and Kurt Langfeld |
|
Relation between chiral symmetry breaking and confinement in YM-theories. |
|
Spectral sums of the Dirac-Wilson operator and their
relation to the Polyakov loop are thoroughly investigated. The
approach by Gattringer is generalized to mode sums which reconstruct
the Polyakov loop locally. This opens the possibility to
study the mode sum approximation to the Polyakov loop correlator.
The approach is re-derived for the ab initio continuum formulation of
Yang-Mills theories, and the convergence of the mode sum is studied
in detail. The mode sums are then explicitly calculated for
the Schwinger model and SU(2) gauge theory in a homogeneous background
field. Using SU(2) lattice gauge theory, the IR dominated mode sums are
considered and the mode sum approximation to the static quark anti-quark
potential is obtained numerically. We find a good agreement between the
mode sum approximation and the static potential at large distances
for the confinement and the high temperature plasma phase.
|
| Phys. Rev. D 77 114018 (2008) |
| pdf file (479 KB) |
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75. | Tobias Kaestner, Georg Bergner, Sebastian Uhlmann, Andreas Wipf, and Christian Wozar |
|
Supersymmetric lattice models in one and two dimensions. |
|
We study and simulate N=2 supersymmetric Wess-Zumino models in one and two
dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to
discretizations of surface integrals. In particular, we check that fermionic and
bosonic masses coincide and the unbroken Ward identities are fulfilled to high
accuracy. Equally good results for the effective masses can be obtained in a model
with the SLAC derivative (even without improvement terms). In two dimensions we
introduce a non-standard Wilson term in such a way that the discretization errors of
the kinetic terms are only of order a squared. Masses extracted from the
corresponding manifestly supersymmetric model prove to approach their continuum
values much quicker than those from a model containing the standard Wilson term.
Again, a comparable enhancement can be achieved in a theory using the SLAC
derivative.
|
| arXiv:0709.0822v2 [hep-lat] |
| pdf file (134 KB) |
| |
| |
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74. | Christian Wozar, Tobias Kaestner, Sebastian Uhlmann,
Andreas Wipf and Thomas Heinzl |
|
Z(3) Polyakov loop models and inverse Monte-Carlo methods. |
|
We study effective Polyakov loop models for SU(3) Yang-Mills theory at finite
temperature. A comprehensive mean field analysis of the phase diagram is carried out
and compared to the results obtained from Monte-Carlo simulations. We find a rich
phase structure including ferromagnetic and antiferromagnetic phases. Due to the
presence of a tricritical point the mean field approximation agrees very well with
the numerical data. Critical exponents associated with second-order transitions
coincide with those of the Z3 Potts model. Finally, we employ inverse Monte-Carlo
methods to determine the effective couplings in order to match the effective models
to Yang-Mills theory.
|
| arXiv:0708.4146v1 [hep-lat] |
| pdf file (127 KB) |
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| |
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73. | Georg Bergner, Tobias Kaestner, Sebastian Uhlmann and Andreas Wipf |
|
Low-dimensional Supersymmetric Lattice Models.
|
|
We study and simulate N=2 supersymmetric Wess-Zumino models in one
and two dimensions. For any choice of the lattice derivative, the theories
can be made manifestly supersymmetric by adding appropriate improvement terms
corresponding to discretizations of surface integrals. In one dimension, our
simulations show that a model with the Wilson derivative and the Stratonovitch
prescription for this discretization leads to far better results at finite
lattice spacing than other models with Wilson fermions considered in the
literature. In particular, we check that fermionic and bosonic masses coincide
and the unbroken Ward identities are fulfilled to high accuracy. Equally good
results for the effective masses can be obtained in a model with the SLAC
derivative (even without improvement terms).
In two dimensions we introduce a non-standard Wilson term in such a way
that the discretization errors of the kinetic terms are only of order O(a4).
Masses extracted from the corresponding manifestly supersymmetric model prove
to approach their continuum values much quicker than those from a model
containing the standard Wilson term. Again, a comparable enhancement can
be achieved in a theory using the SLAC derivative.
|
| Annals Phys. 323 946-988 (2008) |
| pdf file (774 KB) |
| |
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72. | Christian Wozar, Tobias Kaestner, Andreas Wipf and Tom Heinzl |
|
Inverse Monte-Carlo determination of effective lattice models for SU(3)
Yang-Mills theory at finite temperature. |
|
This paper concludes our efforts in describing SU(3)-Yang-Mills theories at different couplings/temperatures in terms of effective Polyakov-loop models. The associated effective couplings are determined through an inverse Monte Carlo procedure based on novel Schwinger-Dyson equations that employ the symmetries of the Haar measure. Due to the first-order nature of the phase transition we encounter a fine-tuning problem in reproducing the correct behavior of the Polyakov-loop from the effective models. The problem remains under control as long as the number of effective couplings is sufficiently small.
|
| Phys. Rev. D 76 085004 (2007) |
| pdf file (179 KB) |
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71. | Franziska Synatschke, Christian Wozar and Andreas Wipf |
|
Spectral sums of the Dirac-Wilson Operator and their
relation to the Polyakov loop. |
|
We investigate and compute spectral sums of the Wilson lattice
Dirac operator for quenched SU(3) gauge theory. It is demonstrated
that there exist sums which serve as order parameters for the
confinement-deconfinement phase transition and get their main
contribution from the IR end of the spectrum. They
are approximately proportional to the Polyakov loop.
In contrast to earlier studied spectral sums some of them
are expected to have a well-defined continuum limit.
|
| Phys. Rev. D75 114003 (2007) |
| pdf file (281 KB) |
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70. | Sebastian Uhlmann, Reinhard Meinel and Andreas Wipf |
|
Ward Identities for Invariant Group Integrals. |
|
We derive two types of Ward identities for the generating functions
for invariant integrals of monomials of the fundamental characters for
arbitrary simple compact Lie groups. The results are applied to the
groups SU(3), Spin(5) and G2 of rank 2 as well as SU(4).
|
| J. Phys. A 40 4367-4389 (2007) |
| pdf file (330 KB) |
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69. | Alexei Abrikosov and Andreas Wipf |
|
The integral form of APS boundary conditions in the Bag Model. |
|
We propose the integral form of Atiah-Patodi-Singer spectral
boundary conditions (SBC) and find explicitly the integral
projector onto SBC for the 3-dimensional spherical cavity. After
discussion of a simple example we suggest that the relation
between the projector and fermion propagator is universal and
stays valid independently of the bag form and space dimension.
|
| J. Phys. A 40 5163-5172 (2007) |
| pdf file (134 KB) |
| |
| |
| |
68. | Andreas Wipf, Tobias Kaestner, Christian Wozar and Tom Heinzl |
|
Generalized Potts-Models and their Relevance for Gauge Theories |
|
We study the Polyakov loop dynamics originating from finite-temperature
Yang-Mills theory. The effective actions contain center-symmetric
terms involving powers of the Polyakov loop, each with
its own coupling. For a subclass with two couplings we
perform a detailed analysis of the statistical mechanics involved.
To this end we employ a modified mean field approximation and
Monte Carlo simulations based on a novel cluster algorithm. We
find excellent agreement of both approaches. The phase
diagram exhibits both first and second order transitions between
symmetric, ferromagnetic and anti-ferromagnetic phases with
phase boundaries merging at three tricritical points. The critical exponents
nu and gamma at the continuous transition between symmetric
and anti-ferromagnetic phases are the same as for the 3-state spin Potts
model.
|
| SIGMA 3 006 (2007) 14 pages |
| pdf file (378 KB) |
| |
| |
| |
67. | Andreas Kirchberg, Klaus Kirsten, Mariel Santangelo and Andreas Wipf |
|
Spectral asymmetry on the ball and asymptotics of the asymmetry kernel |
|
Let i∂ be the Dirac operator on a D=2d dimensional ball
B with radius R. We calculate the spectral asymmetry
η(0,i∂) for D=2 and D=4, when local chiral bag
boundary conditions are imposed. With these boundary conditions,
we also analyze the small-t asymptotics of the heat trace
Tr(F ∂ exp(-t ∂2)) where ∂ is an operator of Dirac type
and F is an auxiliary smooth smearing function.
|
| J. Phys. A 39 9573-9589 (2006) |
| pdf file (178 KB) |
| |
| |
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66. |
Christian Wozar, Tobias Kaestner, Andreas Wipf, Tom Heinzl and Balazs Pozsgay |
|
Phase Structure of Z3-Polyakov-Loop Models |
|
We study effective lattice actions describing the Polyakov loop
dynamics originating from finite-temperature Yang-Mills theory.
Starting with a strong-coupling expansion the effective action is
obtained as a series of Z3-invariant operators
involving higher and higher powers of the Polyakov loop, each with
its own coupling. Truncating to a subclass with two couplings we
perform a detailed analysis of the statistical mechanics involved.
To this end we employ a modified mean field approximation and
Monte Carlo simulations based on a novel cluster algorithm. We
find excellent agreement of both approaches concerning the phase
structure of the theories. The phase diagram exhibits both first
and second order transitions between symmetric, ferromagnetic and
anti-ferromagnetic phases with phase boundaries merging at three
tricritical points. The critical exponents (nu) and (gamma) at
the continuous transition between symmetric and anti-ferromagnetic
phases are the same as for the 3-state Potts model.
|
| Phys. Rev. D 74 114501 (2006) |
| pdf file (714 KB) |
| |
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65 | Tom Heinzl, Ben Liesfeld, Kay-Uwe Amthor, Heinrich Schwoerer,
Roland Sauerbrey and Andreas Wipf |
|
On the observation of vacuum birefringence |
|
We suggest an experiment to observe vacuum birefringence induced by intense laser fields. A high-intensity laser pulse is focused to ultra-relativistic intensity and polarizes the vacuum which then acts like a birefringent medium. The latter is probed by a linearly polarized x-ray pulse. We calculate the resulting ellipticity signal within strong-field QED assuming Gaussian beams. The laser technology required for detecting the signal will be available within the next three years.
|
| Optics Communications 267 318-321 (2006) |
| pdf file (146 KB) |
| |
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64. | Andreas Wipf, Andreas Kirchberg and Dominique Laenge |
|
Algebraic Solution of the Supersymmetric Hydrogen Atom |
|
The N=2 supersymmetric extension of the
Schrödinger-Hamiltonian with 1/r-potential in d dimension is
constructed. The system admits a supersymmetrized Laplace-Runge-Lenz
vector which extends the rotational SO(d) symmetry to a
hidden SO(d+1) symmetry. It is used to determine
the discrete eigenvalues with their degeneracies and
the corresponding bound state wave functions.
(Proceedings of the 4th International Symposium
"Quantum Theory and Symmetries" in Varna, 2005)
|
| in Proceedings 'Quantum Theory and Symmetries', Heron Press (2006),
pages 887-897 |
| pdf-file (91 KB) |
| |
| |
| |
63. | Tom Heinzl, Tobias Kaestner and Andreas Wipf |
|
Effective Lattice Actions for Finite-Temperature Yang-Mills Theory |
|
We determine effective lattice actions for the Polyakov loop using
inverse Monte Carlo techniques.
(Proceedings of the XCQC-Meeting in Swansea, 2005)
|
| hep-th/0504180 |
| pdf-file (243 KB) |
| |
| |
| |
62. | Andreas Wipf |
|
Non-Perturbative Methods in Supersymmetric Theories |
|
The aim of these notes is to provide a short introduction to supersymmetric
theories: supersymmetric quantum mechanics, Wess-Zumino models and
supersymmetric gauge theories. A particular emphasis is put on the
underlying structures and non-perturbative effects in N=1, N=2 and N=4
Yang-Mills theories. (Extended version of lectures given at the TROISIEME
CYCLE DE LA PHYSIQUE EN SUISSE ROMANDE)
|
| hep-th/0504180 |
| pdf-file (394 KB) |
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61. | Tom Heinzl, Tobias Kaestner and Andreas Wipf |
|
Effective Actions for the SU(2) Confinement--Deconfinement Phase
Transition |
|
We compare different Polyakov loop actions yielding effective
descriptions of finite--temperature SU(2) Yang--Mills theory on
the lattice. The actions are motivated by a simultaneous
strong--coupling and character expansion obeying center symmetry
and include both Ising and Ginzburg--Landau type models. To keep
things simple we limit ourselves to nearest--neighbor
interactions. Some truncations involving the most relevant
characters are studied within a novel mean--field approximation.
Using inverse Monte--Carlo techniques based on exact geometrical
Schwinger--Dyson equations we determine the effective couplings of
the Polyakov loop actions. Monte--Carlo simulations of these
actions reveal that the mean--field analysis is a fairly good
guide to the physics involved. Our Polyakov loop actions reproduce
standard Yang--Mills observables well up to limitations due to the
nearest--neighbor approximation.
|
| Phys. Rev. D 72 065005 (2005) |
| pdf file (362 KB) |
| |
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60. | Andreas Kirchberg, Dominique Laenge and Andreas Wipf |
|
From the Dirac Operator to Wess-Zumino Models
on Spatial Lattices |
|
We investigate two-dimensional Wess-Zumino models
in the continuum and on spatial lattices in
detail. We show that a non-antisymmetric
lattice derivative not only excludes chiral
fermions but in addition introduces supersymmetry
breaking lattice artifacts. We study the
nonlocal and antisymmetric SLAC derivative
which allows for chiral fermions
without doublers and minimizes those
artifacts. The supercharges of the
lattice Wess-Zumino models are obtained by dimensional
reduction of Dirac operators in high-dimensional spaces.
The normalizable zero modes of the models with
N=1 and N=2 supersymmetry are counted
and constructed in the weak- and strong-coupling
limits. Together with known methods from operator
theory this gives us complete control of the
zero mode sector of these theories for arbitrary
coupling.
|
| Annals Phys. 316 357-392 (2005) |
| pdf file (169 KB) |
| |
| |
| |
59. | Andreas Kirchberg, Dominique Laenge and Andreas Wipf |
|
Extended Supersymmetries and the Dirac Operator |
|
We consider supersymmetric quantum mechanical
systems in arbitrary dimensions on curved spaces with
nontrivial gauge fields. The square of the Dirac
operator serves as Hamiltonian. We derive a relation between
the number of supercharges that exist and restrictions on the geometry
of the underlying spaces as well as the admissible gauge field
configurations. From the superalgebra with two or more real
supercharges we infer the existence of
integrability conditions and obtain a corresponding superpotential.
This potential can be used to deform the supercharges
and to determine zero modes of the Dirac operator.
The general results are applied to the
Kähler spaces CPN.
|
| Annals Phys. 315 467-487 (2005) |
| pdf file (112 KB) |
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58. | Leander Dittmann, Tom Heinzl and Andreas Wipf |
|
An effective lattice theory for Polyakov loops |
|
We derive effective actions for SU(2) Polyakov loops using
inverse Monte Carlo techniques. In a first approach, we determine the
effective couplings by requiring that the effective ensemble reproduces
the single--site distribution of the Polyakov loops. The latter is flat below the
critical temperature implying that the (untraced) Polyakov loop is distributed
uniformly over its target space, the SU(2) group manifold. This allows
for an analytic determination of the Binder cumulant and the
distribution of the mean--field, which turns out to be approximately
Gaussian. In a second approach, we employ novel lattice
Schwinger--Dyson equations which reflect the SU(2) x SU(2)
invariance of the functional Haar measure. Expanding the effective
action in terms of SU(2) group characters makes the numerics
sufficiently stable so that we are able to extract a total number of 14
couplings. The resulting action is short--ranged and reproduces the
Yang--Mills correlators very well.
|
| JHEP 0406:005,2004 |
---|
| pdf file (317 KB) |
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57. | Leander Dittmann, Tom Heinzl and Andreas Wipf |
|
Effective sigma models and lattice Ward identities |
|
We perform a lattice analysis of the Faddeev--Niemi
effective action conjectured to describe the low--energy sector of
SU(2) Yang--Mills theory. To this end we generate an ensemble of unit
vector fields (`color spins') n from the Wilson action. The
ensemble does not show long--range order but exhibits
a mass gap of the order of 1 GeV. From the distribution of color spins
we reconstruct approximate effective actions by means of exact lattice
Schwinger--Dyson and Ward identities (`inverse Monte Carlo'). We show
that the generated ensemble cannot be recovered from a
Faddeev--Niemi action, modified in a minimal way by adding an explicit
symmetry--breaking term to avoid the appearance of Goldstone modes.
|
| JHEP 0212:014 (2002) |
| pdf file (461 KB) |
| |
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56. | Andreas Kirchberg, Dominique Laenge, Pablo Pisani and Andreas Wipf |
|
Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimension |
|
In this paper the N=2 supersymmetric extension of the Schrödinger
Hamiltonian with 1/r-potential in arbitrary
space-dimensions is constructed. The
supersymmetric hydrogen atom admits a conserved
Laplace-Runge-Lenz vector which extends the
rotational symmetry SO(d) to a hidden SO(d+1)
symmetry. This symmetry of the system is used to
determine the discrete eigenvalues with
their degeneracies and the corresponding bound state wave functions. |
| Annals Phys. 303 359-388 (2003) |
| pdf file (150 KB) |
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55. | Gabriela Beneventano, Mariel Santangelo and Andreas Wipf |
|
Spectral asymmetry for bag boundary conditions |
|
We give an expression,
in terms of boundary spectral functions, for the spectral asymmetry of the
Euclidean Dirac operator in two dimensions, when its domain is determined
by local boundary conditions, and the manifold is of product type. As an
application, we explicitly evaluate the asymmetry in the case of a
finite-length cylinder, and check that the outcome is consistent with our
general result. Finally, we study the asymmetry in a disk, which is a
non-product case, and propose an interpretation. |
| J. Phys. A 35 9343-9354 (2002) |
| pdf file (81 KB) |
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54. | Horacio Falomir, Pablo Pisani and Andreas Wipf |
|
Pole structure of the Hamiltonian zeta-function for a singular potential |
|
We study the pole structure of the zeta-function associated to
the Hamiltonian H of a quantum mechanical particle living in the
half-line R +, subject to the
singular potential g/x 2
+x 2. We show
that H admits nontrivial self-adjoint extensions (SAE) in a given
range of values of the parameter g. The zeta-functions of these
operators present poles which depend on g and, in general, do not
coincide with half an integer (they can even be irrational). The
corresponding residues depend on the SAE considered. |
| J. Phys. A 35 5427-5444 (2002) |
| pdf file (110 KB) |
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53. | Miguel Aguado, Manuel Asorey and Andreas Wipf |
|
Nahm transform and moduli spaces of CPN-models on the torus |
| There is a Nahm transform for two-dimensional gauge fields
which establishes a one-to-one
correspondence between the orbit space of U(N) gauge fields with
topological charge k defined on a torus and that of U(k) gauge
fields with charge N on the dual torus. The main result of this
paper is to show that a similar duality transform cannot exist for
CPN instantons. This fact establishes a significative difference
between 4-D gauge theories and CPN models. The result follows
from the global analysis of the moduli space of instantons based
on a complete and explicit parametrization of all self-dual
solutions on the two-dimensional torus. The boundary of the space
of regular instantons is shown to coincide with the space of
singular instantons. This identification provides a new approach
to analyzing the role of overlapping instantons in the infrared
sector of CPN sigma models. |
| Annals Phys. 298 2-23 (2002) |
| pdf file (330 KB) |
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52. | Pierre van Baal and Andreas Wipf |
|
Classical gauge vacua as knots |
| The four dimensional O(3) non-linear sigma model introduced by Faddeev and
Niemi, with a Skyrme-like higher order term to stabilise static knot solutions
classified by the Hopf invariant, can be rewritten in terms of the complex
two-component CP variables. A further rewriting of these variables in
terms of SU(2) curvature free gauge fields is performed. This leads us to
interpret SU(2) pure gauge vacuum configurations, in a particular maximal
abelian gauge, in terms of knots with the Hopf invariant equal to the winding
number of the gauge configuration. |
| Phys. Lett. B 515 181-184 (2001) |
| pdf file (45 KB) |
| |
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51. | Falk Bruckmann, Tom Heinzl, Temo Vekua and Andreas Wipf |
|
Magnetic monopoles vs. Hopf defects in the Laplacian (Abelian) gauge |
| We investigate the Laplacian Abelian gauge on the sphere
S 4 in the
background of a single `t Hooft instanton. To this end we solve the
eigenvalue problem of the covariant Laplace operator in the adjoint
representation. The ground state wave function serves as an auxiliary
Higgs field. We find that the ground state is always degenerate and has
nodes. Upon diagonalisation, these zeros induce topological defects in
the gauge potentials. The nature of the defects crucially depends on
the order of the zeros. For first-order zeros one obtains magnetic
monopoles. The generic defects, however, arise from zeros of second
order and are pointlike. Their topological invariant is the Hopf index
S 3 --> S 2.
These findings are corroborated by an analysis
of the Laplacian gauge in the fundamental representation where similar
defects occur. Possible implications for the confinement scenario are
discussed. |
| Nucl. Phys. B 593 545-561 (2001) |
| pdf file (111 KB) |
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50. | Chris Ford, Jan Pawlowski, Torsten Tok and Andreas Wipf |
|
ADHM construction of instantons on the torus |
|
We apply the ADHM instanton construction to SU(2) gauge theory on
T 2 n x R 4-n
for n=1,2,3,4. To do this we regard instantons on
T n x R 4-n
as periodic (modulo gauge transformations) instantons on R 4
Since the R 4 topological
charge of such instantons is infinite
the ADHM algebra takes place on an infinite dimensional linear space.
The ADHM matrix M is related to a Weyl operator (with a self-dual background)
on the dual torus T' n.
We construct the Weyl operator corresponding to the
one-instantons on T n x R 4-n.
In order to derive the self-dual potential
on T n x R 4-n
it is necessary to solve a specific Weyl equation. This is
a variant of the Nahm transformation. In the case n=2 (i.e. T x R)
we essentially have an Aharonov Bohm problem on T' 2
In the one-instanton sector we find that the scale parameter,
lambda, is bounded above, lambda 2 V'<4 pi, V'
being the volume of the dual torus T' 2. |
| Nucl. Phys. B 596 387-414 (2001) |
| pdf file (155 KB) |
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49. | Mikhail Volkov and Andreas Wipf |
|
Black hole pair creation in de Sitter space: A complete one-loop analysis |
|
We present an exact one-loop calculation
of the tunneling process in Euclidean quantum gravity
describing creation of black hole pairs in a de Sitter universe.
Such processes are mediated by S 2 x
S 2 gravitational
instantons giving an imaginary contribution to the partition function.
The required energy is provided by the expansion
of the universe. We utilize the thermal properties of de Sitter space
to describe the process as the decay of a metastable thermal
state. Within the Euclidean path integral approach to gravity, we
explicitly determine the spectra of the
fluctuation operators, exactly calculate the one-loop
fluctuation determinants in the zeta-function
regularization scheme, and check the agreement with
the expected scaling behaviour. Our results show a constant volume
density of created black holes at late times, and a very strong
suppression of the nucleation rate for small values of Lambda. |
| Nucl. Phys. B 582 313-362 (2000) |
| pdf file (228 KB) |
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48. | Siyavush Azakov, Hans Joos and Andreas Wipf |
|
Witten-Veneziano relation for the Schwinger model |
| The Witten-Veneziano relation between
the topological susceptibility of pure gauge
theories without fermions and the main contribution
of the complete theory and the corresponding formula
of Seiler and Stamatescu with the so-called contact
term are discussed for the Schwinger model on a circle.
Using the (Euclidean) path integral and the
canonical (Hamiltonian) approaches at finite temperatures
we demonstrate that both formulae give the same result in
the limit of infinite volume and (or) zero temperature. |
| Phys. Lett. B 479 245-258 (2000) |
| pdf file (62 KB) |
| |
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47. | Falk Bruckmann, Tom Heinzl, Andreas Wipf and Torsten Tok |
|
Instantons and Gribov copies in the maximally Abelian Gauge |
| We calculate the Faddeev-Popov operator corresponding to the maximally
Abelian gauge for gauge group SU(N). Specializing to SU(2) we look
for explicit zero modes of this operator. Within an illuminating toy
model (Yang-Mills mechanics) the problem can be completely solved and
understood. In the field theory case we are able to find an analytic
expression for a normalizable zero mode in the background of a single
`t Hooft instanton. Accordingly, such an instanton corresponds
to a horizon configuration in the maximally Abelian gauge. Possible
physical implications are discussed. |
| Nucl. Phys. B 584 589-614 (2000) |
| pdf file (161 KB) |
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46. | Chris Ford, Torsten Tok and Andreas Wipf |
|
SU(N)-gauge theories in Polyakov gauge on the torus |
| We investigate the Abelian projection with respect
to the Polyakov loop operator for
SU(N) gauge theories on the four torus. The gauge fixed
A 0 is time-independent and diagonal.
We construct fundamental domains for A 0.
In sectors with non-vanishing instanton number such gauge fixings
are always singular. The singularities define
the positions of magnetically charged monopoles, strings
or walls. These magnetic defects sit on the Gribov horizon and
have quantized magnetic charges.
We relate their magnetic charges to the instanton number. |
| Phys. Lett. B 456 155-161 (1999) |
| pdf file (79 KB) |
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45. | Chris Ford, Torsten Tok and Andreas Wipf |
|
Abelian projection on the torus for general gauge groups |
| We consider Yang-Mills theories with general gauge groups G
and twists on the four torus. We find consistent boundary conditions
for gauge fields in all instanton sectors.
An extended Abelian projection with respect
to the Polyakov loop operator is presented, where A 0 is independent
of time and in the Cartan subalgebra. Fundamental domains for the
gauge fixed A 0 are constructed for arbitrary gauge groups.
In the sectors with non-vanishing instanton number such gauge fixings
are necessarily singular. The singularities can be restricted to Dirac
strings joining magnetically charged defects.
The magnetic charges of these monopoles take their values
in the co-root lattice of the gauge group.
We relate the magnetic charges of the defects and the
windings of suitable Higgs fields about these defects
to the instanton number. |
| Nucl. Phys. B 548 585-612 (1999) |
| pdf file (167 KB) |
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44. | Chris Ford, Ulrich Mitreuter, Torsten Tok, Andreas Wipf and Jan Pawlowski |
|
Monopoles, Polyakov loops, and gauge fixing on the torus |
| We consider pure Yang Mills theory on the four torus.
A set of non-Abelian transition functions is presented which
encompass all instanton sectors. It is argued that these transition
functions are a convenient starting point for gauge fixing. In
particular, we give an extended Abelian projection with respect
to the Polyakov loop, where A 0 is independent
of time and in the Cartan subalgebra.
In the non-perturbative sectors such gauge fixings
are necessarily singular. These singularities can be restricted to Dirac
strings joining monopole and anti-monopole like `defects'. |
| Annals Phys. 269 26-50 (1998) |
| pdf file (144 KB) |
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43. | Ulrich Mitreuter, Jan Pawlowski and Andreas Wipf |
|
Polyakov loops and fermionic zero-modes in QCD2 on the torus |
| A direct derivation of the free energy
and expectation values of Polyakov-loops in QCD 2 via path integral
methods is given. The chosen gauge fixing has no Gribov-copies and
has a natural extension to four dimensions.The Faddeev-Popov determinant and the
integration over the space component of the gauge field cancel exactly.
It only remains an integration over the zero components of the gauge field
in the Cartan sub-algebra. This way the Polyakov-loop operators become
Vertex-operators in a simple quantum mechanical model. The number of
fermionic zero modes is related to the winding-numbers of A 0 in
this gauge. |
| Nucl. Phys. B 514 381-398 (1998) |
| pdf file (112k) |
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42. | Stefan Durr and Andreas Wipf |
|
Finite temperature Schwinger model with
chirality breaking boundary conditions |
|
The N f-flavour Schwinger Model on a finite space
[ 0 , L ] and subject to bag-type boundary-conditions at
x 1= 0 und x 1= L
is solved at finite temperature T=1/β. The boundary conditions
depend on a real parameter theta and break the axial flavour symmetry.
We argue that this approach is more appropriate to study the broken phases
than introducing small quark masses, since all calculations can be performed
analytically.
In the imaginary time formalism we determine the thermal correlators for
the fermion-fields and the determinant of the Dirac-operator in arbitrary
background gauge-fields. We show that the boundary conditions induce
a CP-odd theta-term in the effective action.
The chiral condensate, and in particular its T- and L- dependence, is
calculated for N f fermions.
It is seen to depend on the order in
which the two lengths β=1/T and L are sent to infinity. |
| Annals Phys. 255 333-361 (1997) |
| pdf file (136 KB) |
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41. | Ivo Sachs and Andreas Wipf |
|
Generalized Thirring models |
| The Thirring model and various generalizations of it are
analyzed in detail. The four-Fermi interaction modifies the equation of state.
Chemical potentials and twisted boundary conditions both result
in complex fermionic determinants which are analyzed. The non-minimal
coupling to gravity does deform the conformal algebra which in particular
contains the minimal models. We compute the central charges,
conformal weights and finite size effects.
For the gauged model we derive the partition functions and the explicit
expression for the chiral condensate at finite temperature and curvature.
The Bosonization in compact curved space-times is also investigated. |
| Annals Phys. 249 380-429 (1996) |
| pdf file (178 KB) |
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40. | Sergei Odintsov and Andreas Wipf |
|
Running surface couplings |
| We discuss the renormalization group improved
effective action and running surface couplings in curved
spacetime with boundary. Using scalar self-interacting
theory as an example, we study the influence of boundary
effects to effective equations of motion in spherical
cap and the relevance of surface running couplings to quantum cosmology
and symmetry breaking phenomenon.
Running surface couplings in the asymptotically free SU(2)
gauge theory are found. |
| Phys. Lett. B 356 26-31 (1995) |
| pdf file (54 KB) |
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39. | Andreas Wipf and Stefan Durr |
|
Gauge theories in a bag |
| We investigate multi-flavour gauge theories confined
in d=2n-dimensional Euclidean bags. The boundary conditions for the 'quarks'
break the axial flavour symmetry and depend on a parameter theta
We determine the theta-dependence of the fermionic correlators
and determinants and find that a CP-breaking theta-term is generated
dynamically. As an application we calculate the chiral
condensate in multi-flavour QED2 and
the abelian projection of QCD2.
In the second model a condensate is generated
in the limit where the number of colours, Nc,
tends to infinity. We prove that the condensate in QCD2
decreases with increasing bag radius R at least as
R -1/NcNf.
Finally we determine the correlators of mesonic currents in
QCD2. |
| Nucl. Phys. B 443 201-232 (1995) |
| pdf file (149 KB) |
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38. | Viatcheslav Mukhanov, Andreas Wipf and Andrei Zelnikov |
|
On 4-D Hawking Radiation From Effective Action |
|
We determine the s-waves contribution
of a scalar field to the four dimensional effective action
for arbitrary spherically symmetric external
gravitational fields. The result is applied to 4d-black
holes and it is shown that the energy momentum tensor
derived from the (nonlocal) effective action contains
the Hawking radiation. The luminosity is close to
the expected one in the s-channel. The energy momentum
tensor may be used as starting point to study the
backreaction problem. |
| Phys. Lett. B 332 283-291 (1994) |
| pdf file (92 KB) |
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37. | Viatcheslav Mukhanov and Andreas Wipf |
|
On the symmetries of Hamiltonian systems |
| In this paper we show how the well-known
local symmetries of Lagrangean
systems, and in particular the diffeomorphism invariance, emerge
in the Hamiltonian formulation. We show that only the constraints
which are linear in the momenta generate transformations which correspond
to symmetries of the corresponding Lagrangean system. The nonlinear
constraints (which we have, for instance, in gravity,
supergravity and string theory) rather generate the dynamics of the
corresponding Lagrangean system. Only in a very special combination
with "trivial" transformations proportional to the equations of motion
do they lead to symmetry transformations. We reveal the importance
of these special "trivial" transformations for the interconnection
theorems which relate the symmetries of a system with its dynamics.
We prove these theorems for general Hamiltonian systems. We
apply the developed formalism to concrete physically relevant systems
and in particular those which are diffeomorphism invariant.
The connection between the parameters of the symmetry transformations
in the Hamiltonian- and Lagrangean formalisms is found.
The possible applications of our results are discussed. |
| Int. J. Mod. Phys. A 10 579-610 (1995) |
| pdf file (127 KB) |
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36. | Ivo Sachs and Andreas Wipf |
|
Temperature and curvature dependence of the chiral
symmetry breaking in 2-D gauge theories |
| The partition function and the order parameter for
the chiral symmetry breaking are computed for a family of
2-dimensional interacting theories containing the gauged Thirring
model. In particular we derive non-perturbative expressions for
the dependence of the chiral condensate on the temperature
and the curvature. Both, high temperature and high curvature suppress
the condensate exponentially and we can associate an effective
temperature to the curvature. |
| Phys. Lett. B 326 105-110 (1994) |
| pdf file (68 KB) |
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35. | Laszlo Feher, Lochlainn O'Raifeartaigh, Philippe Ruelle, Izumi Tsutsui and Andreas Wipf |
|
On Hamiltonian Reductions Of The Wess-Zumino-Novikov-Witten Theories |
| The structure of Hamiltonian reductions of the
Wess-Zumino-Novikov-Witten (WZNW) theory by first class Kac-Moody
constraints is analyzed in detail. Lie algebraic conditions
are given for ensuring the presence of exact integrability,
conformal invariance and W-symmetry in the reduced theories.
A Lagrangean, gauged WZNW implementation of the reduction
is established in the general case and thereby
the path integral as well as the BRST formalism are
set up for studying the quantum version of the reduction.
The general results are applied to a number of examples.
In particular, a W-algebra is associated to each
embedding of sl(2) into the simple Lie algebras by using
purely first class constraints. The importance of these
sl(2) systems is demonstrated by showing that they underlie
the Wn l-algebras
as well. New generalized Toda theories are found whose chiral algebras
are the W-algebras belonging to the half-integral sl(2) embeddings,
and the W-symmetry of the effective action of those
generalized Toda theories associated with the integral
gradings is exhibited explicitly. |
| Phys. Rept. 222 1-64 (1992) |
| pdf file (228 KB) |
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34. | Ivo Sachs, Andreas Wipf and Arne Dettki |
|
Conformal And Thermodynamic Properties Of A Family Of Thirring Like Model |
|
We investigate Thirring-like models containing fermionic and
scalar fields propagating in 2-dimensional space
time. The corresponding conformal algebra is studied and we disprove
a conjecture relating the finite size effects to the central charge.
Some new results concerning the fermionic determinant on the torus
with chirally twisted boundary conditions and a chemical
potential are presented. In particular we show how the thermodynamics
of the Thirring model depends on the current-current interaction. |
| Phys. Lett. B 317 545-549 (1993) |
| pdf file (66 KB) |
| |
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33. | Claus Kiefer and Andreas Wipf |
|
Functional Schrödinger equation for fermions in external gauge fields |
| We discuss the functional Schrödinger picture for fermionic fields in
external gauge fields for both stationary and time - dependent problems. We
give formal results for the ground state and the solution of the time -
dependent Schrödinger equation for QED in arbitrary dimensions, while more
explicit results are obtained in two dimensions. For both the massless and
massive Schwinger model we give an explicit expression for the ground state
functional as well as for the expectation values of energy, electric and axial
charge. We also give the corresponding results for non-abelian fields. We solve
the functional Schrödinger equation for a constant external field in four
dimensions and obtain the amount of particle creation. We solve the
Schrödinger equation for arbitrary external fields for massless QED in two
dimensions and make a careful discussion of the anomalous particle creation
rate. Finally, we discuss some subtleties connected with the interpretation of
the quantized Gauss constraint. |
| Annals Phys. 236 241-285 (1994) |
| pdf file (148 KB) |
| |
| |
| |
32. | Christian Wiesendanger and Andreas Wipf |
|
Running Coupling Constants From Finite Size Effects |
|
The dependence of effective actions on the finite size
of the space-time region M is investigated in detail.
It is shown explicitly that the one-loop effective actions
on M and lambda x M are the same if the volume and surface coupling
constants and fields scale according to the renormalization flow.
An efficient algorithm for calculating the beta-functions and
anomalous dimensions is derived. The general results are applied to a
number of examples, in particular scalar field theories in two,
four and six dimensions, O(N)-sigma models in two dimensions and
gauge field theories with fermions in two and four dimensions. |
| Annals Phys. 233 125-161 (1994) |
| pdf file (131 KB) |
| |
| |
| |
31. | Lochlainn O'Raifeartaigh, Norbert Straumann and Andreas Wipf |
|
Aharonov-Bohm Effect In Presence Of Superconductors |
| The analysis of a previous paper, in which it
was shown that the energy for the Aharonov-Bohm effect could be
traced to the interaction energy between the magnetic field of the
electron and the background magnetic field, is extended to cover the
case in which the magnetic field of the electron is shielded from
the background magnetic field by superconducting material. The
paradox that arises from the fact that such a shielding would
apparently preclude the possibility of an interaction energy is
resolved and, within the limits of the ideal situation considered,
the observed experimental result is derived. |
| Found. Phys. 23 703-709 (1992) |
| pdf file (140 KB) |
| |
| |
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30. | Lochlainn O'Raifeartaigh, Norbert Straumann and Andreas Wipf |
|
On The Origin Of The Aharonov-Bohm Effect |
| It is now generally accepted that the Aharanov-Bohm effect
originates in the interaction between an electron and an external
gauge-potential A whose B-field vanishes locally. Here it is shown
that the effect can equally well be regarded as originating
in the interaction of the magnetic field of the electron with
the distant B field. From this point of view the effect is seen
to have a natural classical origin and loses much of its mystery. |
| Comments Nucl. Part. Phys. 20 15-22 (1991) |
| pdf file (466 KB) |
| |
| |
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29. | Ivo Sachs and Andreas Wipf |
|
Finite Temperature Schwinger Model |
|
The temperature dependence of the order parameter of the Schwinger model
is calculated in the euclidean functional integral approach. For that we
solve the model on a finite torus and let the spatial extension
tend to infinity at the end of the computations. The
induced actions, fermionic zero-modes, relevant Green functions
and Wilson loop correlators on the torus are derived. We find
the analytic form of the chiral condensate for any temperature and
in particular show that it behaves like
-2e -pi sqrt(pi)T/e
for temperatures large compared to the induced photon mass. |
| Helv. Phys. Acta 65 652-678 (1992) |
| pdf file (225 KB) |
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28. | Arne Dettki and Andreas Wipf |
|
Finite Size Effects From General Covariance And Weyl Anomaly |
| By exploiting the diffeomorphism invariance we relate the
finite size effects of massless theories to their Weyl anomaly.
We show that the universal contributions to the finite size
effects are determined by certain coefficient functions in the heat
kernel expansion of the related wave operators. For massless
scalars confined in a 4-dimensional curved spacetime with
boundary the relevant coefficients are given confirming the results
of Moss and Dowker and also of Branson and Gilkey.
We apply the general results to theories on bounded regions in two- and
four-dimensional flat space-times and determine the change of the
effective action under arbitrary conformal deformations of the regions. |
| Nucl. Phys. B 377 252-280 (1992) |
| pdf file (108 KB) |
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27. | Laszlo Feher, Lochlainn O'Raifeartaigh, Philippe Ruelle, Izumi Tsutsui and Andreas Wipf |
|
Generalized Toda Theories And W Algebras Associated With Integral Gradings |
| A general class of conformal Toda theories associated
with integral gradings of the simple Lie algebras is investigated.
These generalized Toda theories are obtained by reducing the
Wess-Zumino-Novikov-Witten (WZNW) theory by first class constraints,
and thus they inherit extended conformal symmetry algebras, generalized
W-algebras, and current dependent Kac-Moody (KM) symmetries from the
WZNW theory, which are analysed in detail in a non-degenerate
case. WE uncover the sl(2) structure underlying the generalized
W-algebras, which allows for identifying the primary fields, and give a simple
algorithm for implementing the W-symmetries by current dependent KM
transformations, which can be used to compute the action of the
W-algebra on any quantity. We establish how the Lax pair of Toda theory
arises in the WZNW framework and show that a recent result of
Mansfield and Spence, which interprets the W-symmetry of the Toda theory
by means of non-Abelian form preserving gauge transformations of the Lax
pair, arises immediately as a consequence of the KM interpretation.
|
| Annals Phys. 213 1-20 (1992) |
| pdf file (88 KB) |
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26. | Lochlainn O'Raifeartaigh, Philippe Ruelle, Izumi Tsutsui and Andreas Wipf |
|
W algebras for generalized Toda theories |
|
The generalized Toda theories obtained in a previous paper
by the conformal reduction of WZNW theories possess a new class of
W-algebras, namely the algebras of gauge-invariant polynomials of the
reduced theories. An algorithm for the construction of base-elements for
the W-algebras of all such generalized Toda theories is found, and
the W-algebras for the maximal SL(N,R) generalized Toda theories are
constructed explicitly, the primary field basis being identified.
|
| Commun. Math. Phys. 143 333-354 (1992) |
| pdf file /93 KB) |
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25. | Lochlainn O'Raifeartaigh and Andreas Wipf |
|
Conformally Reduced WZNW Theories And Two-Dimensional Gravity |
|
The WZNW theories (for a non-compact form of the
gauge groups) are reduced to a series of integrable theories that
interpolate between WZNW theories and the corresponding
Toda theories. They describe a set of WZNW fields in interaction
with each other and with a two-dimensional gravitational field.
An algorithm for constructing the general
solutions, and a formula that relates the Virasoro and Kac-Moody
centres of the reduced theories is given, together with a
(conformally non-invariant) extension of the reduction to obtain
affine Toda theories. |
| Phys. Lett. B 251 361-368 (1990) |
| pdf file (74 KB) |
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24. | Janos Balog, Laszlo Feher, Peter Forgacs, Lochlainn O'Raifeartaigh and Andreas Wipf |
|
Kac-Moody Realization Of W Algebra |
| By realizing the W-algebras of
Toda field-theories as the algebras of
gauge-invariant polynomials of constrained Kac-Moody
systems we obtain a simple algorithm for constructing W-algebras
without computing the W-generators themselves.
In particular this realization yields an identification of a
primary field basis for all the W-algebras, quadratic bases
for the A,B,C-algebras, and the relation of
W-algebras to Casimir algebras.
At the quantum level it yields the
general formula for the Virasoro centre
in terms of the KM- level. |
| Phys. Lett. B 244 435-441 (1990) |
| pdf file (66 KB) |
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23. | Janos Balog, Laszlo Feher, Lochlainn O'Raifeartaigh, Peter Forgacs and Andreas Wipf |
|
Toda Theory And W Algebra From A Gauged WZNW Point Of View |
| Annals Phys. 203 76-136 (1990) |
|
A new formulation of Toda theories is proposed by showing that they can
be regarded as certain gauge Wess-Zumino-Novikov-Witten (WZNW) models.
It is argued that the WZNW variables are the proper ones for Toda
theory, since all the physically permitted Toda solutions are regular
when expressed in these variables. A detailed study of classical
Toda theories and their W-algebras is carried out from this unified
WZNW point of view. WE construct a primary field basis for the W-algebra
for any group, we obtain a new method for calculating the W-algebra
and it action on the Toda fields by constructing its Kac-Moody
implementation, and we analyse the relationship between W-algebras
and Casimir algebras. The W-algebra of G 2
and the Casimir algebras for the classical groups are exhibited explicitly.
|
| Annals Phys. 203 76-136 (1990) |
| pdf file (182 KB) |
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22. | Peter Forgacs, Andreas Wipf, Janos Balog, Laszlo Feher and Lochlainn O'Raifeartaigh |
|
Liouville and Toda Theories as Conformally Reduced WZNW Theories |
| It is shown that the Liouville theory can be regarded
as an SL(2,R) Wess-Zumino-Novikov-Witten theory with conformal
invariant constraints and that Polyakov's SL(2,R) Kac-Moody symmetries
of induced two-dimensional gravity is just one side of the
WZNW current algebra. Analogously, Toda field theories can be
regarded as conformal-invariantly constrained WZNW theories for
appropriate (maximally non-compact) groups.
|
| Phys. Lett. B 227 214-220 (1989) |
| pdf file (69 KB) |
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21. | Emil Mottola and Andreas Wipf |
|
Unsuppressed Fermion Number Violation at High Temperature: An O(3) Model |
| The O(3) nonlinear sigma-model in 1+1 dimensions,
modified by an explicit symmetry-breaking term, is presented
as a model for baryon- and lepton-number violation in the standard
electroweak theory. Although arguments bases on the
Atiyah-Singer index theorem and instanton physics apply to the
model, we show by explicit calculations that the rate of
chiral fermion-number violation due to the axial anomaly
is entirely unsuppressed at sufficiently high temperatures.
Our results apply to unbroken gauge theories as well and may
require reevaluation of the role of instantons in high-temperature QCD.
|
| Phys. Rev. D 39 588-602 (1989) |
| pdf file (2698 KB) |
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20. | Janos Balog, Lochlainn O'Raifeartaigh, Peter Forgacs and Andreas Wipf |
|
Consistency of String Propagation on Curved Spacetimes: An SU(1,1) based Counterexample |
|
String propagation on non-compact group
manifolds is studies as an exactly solvable example of propagation
on more general curved spacetimes. It is shown that for the only
viable group SU(1,1) x G c string propagation is
consistent classically but not quantum mechanically (unitarity is violated).
This shows that conformal invariance of the corresponding sigma-model
(vanishing of the beta-functions) is not sufficient to guarantee
unitarity.
|
| Nucl. Phys. B 325 225-241 (1989) |
| pdf file (528 KB) |
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18. | Steven Blau, Matt Visser and Andreas Wipf |
|
Analytical Results for the Effective Action |
|
We study the coupling of scalar fields and Dirac spinors to classical
background gauge potentials. For the zero-field and constant-field
configurations we derive some analytic expressions for the one-loop
effective action. We discuss both massless and massive scalars
and spinors. These results extend toe work of Schwinger and others
|
| Int. Journ. Mod. Phys. A 6 5408-5434 (1992) |
| pdf file (1062 KB) |
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17. | Steven Blau, Matt Visser and Andreas Wipf |
|
Zeta Functions and the Casimir Energy |
|
We use zeta functions techniques to give a finite definition
for the Casimir energy of an arbitrary ultrastatic spacetime
with or without boundaries. We find that the Casimir energy
is intimately related to, but not identical to, the one-loop
effective energy. We show that in general the Casimir energy
depends on a normalization scale. This phenomenon has relevance
to applications of the Casimir energy in bag models of QCD
Within the framework of Kaluza-Klein models we discuss the one-loop
corrections to the induced cosmological and Newton constants in
terms of a Casimir like effect.We can calculate the
dependence of these constants on the radius of the compact
dimensions, without having to resort to detailed calculations.
|
| Nucl. Phys. B 310 163-180 (1988) |
| pdf file (98 KB) |
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16. | Steven Blau, Matt Visser and Andreas Wipf |
|
Determinants of Conformal Wave Operators in Four Dimensions |
|
We consider conformally coupled wave operators in four dimensions.
Such operators are associated with conformally coupled massless
scalars, massless spin 1/2 particles and Abelian gauge bosons.
We explicitly calculate the change in the determinant of
these wave operators as a function of conformal deformations
of the background metric. This variation is given in terms
of a geometrical object, the second Seeley-de Witt coefficient.
|
| Phys. Lett. B 209 209-213 (1988) |
| pdf file (252 KB) |
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15. | Steven Blau, Matt Visser and Andreas Wipf |
|
Determinants, Dirac Operators and One-Loops Physics |
| We consider the Dirac operator. Its determinant
is examined and in two Euclidean dimensions is explicitly
evaluated in terms of geometrical quantities. This leads us
to consider a generalization of the Wess-Zumino action that is
applicable to arbitrary genus. Our analysis is relevant to
a number of interesting systems: Schwinger models on curved
two-manifolds; string theories with world-sheet vectors;
and as an exploration of possible directions in evaluating
determinants in four dimensions.
|
| Int. J. Mod. Phys. A 4 1467-1484 (1989) |
| pdf file (540 KB) |
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14. | Fred Cooper, Avinash Khare, Renato Musto and Andreas Wipf |
|
Supersymmetry and the Dirac Equation |
|
We discuss in detail two supersymmetries of the 4-dimensional
Dirac operator D2 where
D=d-ieA, namely the usual chiral supersymmetry and a separate
complex supersymmetry. Using SUSY methods developed to categorize
solvable potentials in 1-dimensional quantum mechanics we systematically
study the cases where the spectrum, eigenfunctions, and S-matrix
of D2 can be obtained
analytically. We relate these solutions to the solutions of the
ordinary massive Dirac equation in external gauge fields. We show
that whenever a Schrödinger equation for a potential V(x)
is exactly solvable, then there always exists a corresponding
static scalar field phi(x) for which the Jackiw-Rebbi type (1+1)-dimensional
Dirac equation is exactly solvable with V(x) and φ(x) being related by
V(x)=φ2(x)+φ'(x). We also
discuss and exploit the supersymmetry of the path integral representation
for the fermion propagator in an external field.
|
| Annals of Phys. 187 1-28 (1988) |
| pdf file (1113 KB) |
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13. | Fred Cooper, Joseph Ginnochio and Andreas Wipf |
|
Supersymmetry, Operator Transformations and Exactly Solvable Potentials |
| A large class of potentials can be solved by using
supersymmetry and shape invariance. In this paper we apply operator
transformations (f transformations) to these algebraically solvable
problems to obtain a larger class of solvable potentials -
the Natanzon class of potentials which are not shape invariant.
The important condition (which is independent of supersymmetry)
for finding new potentials from old ones using operator
transformations is that the resulting Schödinger equation
has a potential which does not depend on the state. As a
special case of the f transformation we rederive the previously
known connection between the 2d harmonic oscillator, the
hydrogen atom and the Morse potential. We also discuss the lack
of commutivity of SUSY and the f transformations.
|
| J. Phys. A 22 3707-3716 (1989) |
| pdf file (438 KB) |
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12. | Fred Cooper, Joseph Ginnochio and Andreas Wipf |
|
Derivation of the S-Matrix using Supersymmetry
|
---|
|
Using supersymmetry and shape invariance the reflection
and transmission coefficients for a large class of
solvable potentials can be obtained algebraically.
|
| Phys. Lett. A 129 147-147
(1988) |
| pdf file (167 KB) |
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11. | Lochlainn O'Raifeartaigh and Andreas Wipf |
|
WKB Properties of the Time Dependent
Schrödinger System |
| It is shown that the time-dependent WKB expansion
highlights some of the hidden properties of the Schrödinger
equation and forms a natural bridge between that equation and
the functional integral formulation of quantum mechanics.
In particular it is shown that the leading (zero- and first-order in
h) terms in the WKB expansion are essentially classical, and the
relationship of this result to the classical nature of the WKB
partition function, and of the anomalies in quantum field theory,
is discussed.
|
| Found. Phys. 18 307-329 (1988) |
| pdf file (986 KB) |
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10. | Peter Forgacs, Lochlainn O'Raifeartaigh and Andreas Wipf |
|
Scattering Theory, U(1)-Anomaly and Index Theorems for
Compact and Non-Compact Manifolds |
|
The L2 index theorem on even dimensional non-compact manifolds
is related to the corresponding APS result for compact manifolds
with boundaries. We show that generally the two index theorems
are slightly different. For the two-dimensional Dirac operator
on the disk we formulate (modified) nonlocal boundary conditions
such that the two index theorems coincide. Exploiting the
supersymmetric structure of D2 operator we
explicitly evaluate the supersymmetric partition function in this case.
|
| Nucl. Phys. B 293 559-592 (1987) |
| pdf file (1190 KB) |
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9. | Renato Musto, Lochlainn O'Raifeartaigh and Andreas Wipf |
|
The U(1)-Anomaly, the Non-Compact Index Theorem, and the (Supersymmetric) BA-Effect |
|
The fractional discrepancy between the global U(1) chiral anomaly (described
by a flux-integral of gauge-fields and not necessarily an integer
on non-compact, euclidean space-times) and the index of the
Dirac operator D is shown to be just
(δ+(0) - δ-(0))/π where
δ+(0) and δ-(0) are the
left- and right-handed zero energy phase shifts.
|
| Phys. Lett. B 175 433-438 (1986) |
| pdf file (684 KB) |
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8. | Yasushi Fujimoto, Hiroshi Yoneyama and Andreas Wipf |
|
Symmetry Restoration of Scalar Models at Finite Temperature |
|
The symmetry restoration of scalar models at finite temperature
and in less than four dimensions is investigated. For that
purpose a series of approximations to the constraint effective
lattice-potential is introduced. The continuum limit of these
mean-field-like potentials is discussed and it is
shown that the symmetry is always restored at finite
temperature. As an application we derive an estimate
for the critical temperature.
|
| Phys. Rev. D 38 2625-2634 (1988) |
| pdf file (1678 KB) |
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7. | Yasushi Fujimoto, Hiroshi Yoneyama and Andreas Wipf |
|
Finite Temperature lambda φ 4-Theory
in Two and Three Dimensions and Symmetry Restoration |
|
lambda φ4 theory is studied in 2 and
3 dimensions to examine the validity of the finite temperature
perturbation theory. We find that in some cases
it is good even at high temperature in contrast to the case in
4 dimensions. We also discuss the problem of symmetry
restoration and show an example of symmetry restoration
within a save perturbation at high temperature.
|
| Z. Phys. C 35 351-354 (1987) |
| pdf file (246 KB) |
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6. | Andreas Wipf |
|
Some Results on Magnetic Monopoles and Vacuum Decay |
| PhD-Thesis
- 1. Introduction
- 2. Magnetic monopoles
- 3. Explicit monopole solutions
- 4. The WKB-exponent in field theory
- 5. The primed determinant
|
| Helv. Phys. Acta 58 531-596 (1985) |
| pdf file (38 MB) |
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5. | Andreas Wipf |
|
Non-Relativistic Yang-Mills Particles in a Spherically Symmetric Monopole Field |
|
We discuss the equations of motion and the conservation laws for a
non-relativistic isospin carrying particle in a spherically symmetric monopole
field and for a vanishing Yukawa coupling. In the 't Hooft-Polyakov monopole
field we find no classical counterpart of the Rubakov effect. In the
Prasad-Sommerfield limit we can solve the equations of motion
analytically.
|
| J. Phys. A 18 2379-2384 (1985) |
| pdf file (226 KB) |
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4. | Lochlainn O'Raifeartaigh, Andreas Wipf and Hiroshi Yoneyama |
|
The Constraint Effective Potential |
|
Because of the non-perturbative nature of the conventional
effective potential Γ(Ω,φ) (for classical Higgs potentials
and volume Omega) and because of the inconvenience of a
Legendre transform for numerical computations, it is proposed
to replace Γ(Ω,φ) by a "constraint" effective potential
U(Ω,φ), which has a direct intuitive meaning, which is
very convenient for lattice computations, and from which
Γ(Ω,φ) can immediately be recovered (as the convex hull).
In particular, Γ(∞,φ)=U(∞,φ). Various properties
of U(Ω,φ), such as convexity properties, upper and lower
bounds and volume dependence are established. It is computed
directly for zero dimensions and by Monte Carlo simulations
in one and four dimensions, with up to 160 and 84
lattice sites, respectively.
|
| Nucl. Phys. B 271 653-680 (1986) |
| pdf file (1420 KB) |
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3. | Andreas Wipf |
|
Tunnel Determinants |
|
Methods for computing the regularized determinants of fluctuation operators
are being developed. The results follow from the fact that these determinants
can be expressed by eigenmodes of the fluctuation operator. As an application
the tunnel determinants of some one- and higher-dimensional models are
computed. It is shown that every fluctuation operator defines
a supersymmetric quantum mechanical system.
|
| Nucl. Phys. B 269 24-44 (1986) |
| pdf file (703 KB) |
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2. | Andreas Wipf |
|
Upper and Lower Bounds For The Bounce Action |
|
We show how to bound the WKB exponent in field theory from above
and below. The results follow from an inf-max characterisation of the
Euclidean action of the bounce solution. For the lower bounds
our method involves only some simple inequalities while for the
upper bounds it leds to a finite dimensional extremising problem.
We apply this method to approximate the WKB exponent for the
effective potential in 1-loop approximation which is used in the
inflationary cosmological models.
|
| J. Phys. A 18 2521-2529 (1985) |
| pdf file (310 KB) |
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1. | Martin Schweizer, Norbert Straumann and Andreas Wipf |
|
Postnewtonian Generation Of Gravitational Waves In A Theory Of Gravity With Torsion |
| We adapt the post-Newtonian gravitational-radiation
methods developed within general relativity by Epstein and Wagoner
to the gravitation theory with torsion, recently proposed
by Hehl et al., and show that the two theories predict in this
approximation the same gravitational radiation losses. Since they agree
also on the first-Newtonian level, they are at the present time - observationally -
indistinguishable.
|
| Gen. Rel. and Grav. 12 951-961 (1980) |
| pdf file (446 KB) |
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