Dr. habil. Georg Bergner
Room: Abb 202
My main current investigations are related to lattice gauge theory and, more general, quantum field theory on the lattice. I am using numerical computations to study properties of quantum field theories such as particle masses and phase transitions. The approach is based on a representation of the theory on a space-time lattice. Monte-Carlo simulations provide an insight into the nonperturbative sector of the quantum field theory. Especially gauge theories with dynamical fermions like QCD and supersymmetric Yang-Mills theory in four dimensions are complex systems. They require large scale computer resources. Therefore, I am doing the computations and code development on large scale computing facilities such as provided by the Jülich Supercomputing Centre.
Investigations of quantum chromodynamics (QCD) at finite temperature and finite density are the new challenging topic of my investigations. Lattice computations provide a successful approach to investigate strongly interacting theories like QCD. Unfortunately a severe sign problem prohibits an application of this approach at finite density. I am investigating effective models that can be derived from a strong coupling expansion of lattice QCD. These models help to find predictions for QCD at finite density. They provide also a playground for methods to understand and attack the sign problem.
Possible extensions of the standard model of quantum field theory have been a major topic of my research and I am still interested and involved in these investigations. I started with models similar to the matter sector of supersymmetric extensions of the standard model (Wess-Zumino models). Later on I began to consider the correpsonding gauge sector (supersymmetric Yang-Mills theory) as well. Supersymmetry requires the simulation of dynamical fermions on the lattice. Therefore the simulations are similar to QCD on the lattice (with one quark flavour). Unbroken supersymmetry predicts a degeneracy of the fermionic and bosonic energy states. Consequently, each bosonic particle should have a fermionic partner with the same mass. In principle, the mass degeneracy should be obtained also in the numerical lattice simulations. However, the lattice breaks supersymmetry. More precisely, I was able to establish a No-Go theorem stating that either supersymmetry or locality must be broken in a lattice theory. The re-establishment of supersymmetry in the continuum limit of the lattice theory is the main goal of my lattice simulations. Therefore, I am studying the masses of the particles in supersymmetric Yang-Mills theory.
The simulation supersymmetric Yang-Mills and lattice QCD requires advanced numerical methods. Considerations and extensions of these methods are therefore an essential part for my studies. In that context I have studied methods for the calculation of the lowest real eigenmodes of large sparse matrices (the Dirac-Wilson operator). These are needed, for example, to obtain the Pfaffian sign in supersymmetric Yang-Mills theory. The measurement of the observables in supersymmetric Yang-Mills theory is also a challanging task. It requires advanced techniques for the glueball operators and meson operators with diconnected contributions.
I am investigating if a similar solution as for the chiral symmetry on the lattice can be found for supersymmetry. Like supersymmetry, the chiral symmetry can not be represented on the lattice in a straight forward way. The solution is a renormalization group step that maps the continuum theory onto the lattice. The symmetry is expressed in terms of a relation on the lattice (Ginsparg-Wilson relation). I have generalized this approach for an arbitrary symmetry (including supersymmetry).
Since there is no straight forward implementation of supersymmetry on the lattice it is helpful to compare the results with other methods. The functional renormalization group flow offers an interesting non-perturbative method as alternative for the lattice simulation. Therefore a comparison of these methods is one of my current research interests.