Twenty-seven years after the inception of QCD its low-energy features are still not fully understood. The two main problems are the spontaneous breakdown of chiral symmetry and confinement. While the former is reasonably well described by the instanton vacuum, the property of confinement remains somewhat elusive. Nonetheless, the last few years have seen some remarkable progress in this direction. With the work of Seiberg and Witten there is now an exact non-perturbative solution of a strongly coupled gauge theory in four dimensions, though in a supersymmetric setting. This work has leant new support to the old idea of describing the vacuum as a dual superconductor where confinement is due to monopole condensation and a dual Meissner effect. In addition, lattice calculations using (variants of) 't Hooft's maximal abelian gauge fixing find that abelian and monopole fields are the dominant configurations in the path integral (abelian and monopole dominance). It is, however, difficult to confirm these results in a gauge independent way. Depending on the gauge chosen, there are alternative confinement mechanisms (like e.g. vortex percolation). In addition, the relation to the instanton vacuum remains to be further investigated.
Without simplifying assumptions like supersymmetry, it is rather difficult to confirm the lattice results analytically. Already on the kinematical level one has to deal with the issues of gauge fixing ambiguities, the Gribov problem and the like. A theoretical description of the confinement dynamics starting from first principles at present seems rather hopeless. Thus, for the time being, one has to rely on the respectable tradition of model building and effective field theories. One particular candidate of these, the dual Abelian Higgs model, has recently been shown to lead to an effective 4d string theory of confinement.
Remarkably, also from the pure string theory side there is now a route towards confinement via the celebrated AdS/CFT correspondence. Using effective supergravity models one can study the large-N sector of gauge theories, in particular Wilson loops, glueballs and even the shape of the flux tube. More recently, it was observed that string vacua with a nonvanishing B-field induce a noncommutative deformation of the spacetime structure underlying effective Yang-Mills theories on branes.
It thus seems that, after a long period of divergence, gauge field and string theory are again converging towards each other.
Time | Name | Title | |
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14:00 - 14:10 | Opening | ||
14:10 - 15:00 | Asorey | Monopoles, Gauge Fixing and Confinement | |
15:00 - 15:50 | Müller-Preussker | Lattice Gauge Theories with Boundary Conditions | |
15:50 - 16:10 | Coffee Break | ||
16:10 - 17:00 | Bruckmann | Instantons and Monopoles in Abelian Projections | |
17:00 - 17:50 | Reinhardt | Magnetic Vortices in Yang-Mills Theory | |
17:50 - 18:10 | Coffee Break | ||
18:10 - 19:00 | Pepe | Nature and Properties of Center Vortices |
Time | Name | Title |
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09:00 - 09:50 | Langfeld | Realization of Confinement in Novel Gauges |
09:50 - 10:40 | Heinzl | Instantons and Gribov Copies in the Maximally Abelian Gauge |
10:40 - 11:00 | Coffee Break | |
11:00 - 11:50 | Thies | On the Phase Structure of the 't Hooft Model |
11:50 - 12:40 | Stamatescu | On the Topological Structure of the Yang-Mills Vacuum - Problems and Results of Lattice Simulations |
12:40 - 14:00 | Lunch Break |
Time | Name | Title | |
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14:00 - 14:50 | Zakharov | Power Corrections from Short Distances in QCD | |
14:50 - 15:40 | Weiss | QCD Instantons and Zero Modes in Hard Scattering Processes | |
15:40 - 16:00 | Coffee Break | ||
16:00 - 16:50 | Polonyi | Renormalization of Periodic Potentials | |
16:50 - 17:40 | Smilga | Normalized Vacuum States in Supersymmetric Matrix Models with any Gauge Group | |
17:40 - 18:00 | Coffee Break | ||
18:00 - 18:50 | Ketov | Exact Multi-Monopole Moduli Space Metrics from Superspace |
Time | Name | Title |
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09:00 - 09:45 | Brandhuber | The Coulomb Branch of Gauge Theories in the AdS/CFT Correspondence |
09:45 - 10:30 | Sachs | Field Theory and Non-BPS States in String Theory |
10:30 - 10:50 | Coffee Break | |
10:50 - 11:35 | Mansfield | AdS/CFT and the Schrödinger Functional |
11:35 - 12:20 | Theisen | Field Theory Anomalies from the AdS/CFT Correspondence |
12:20 - 12:40 | Coffee Break/Snacks | |
12:40 - 13:25 | Strobl | Introduction to Poisson Sigma Models |
13:25 - 14:10 | Klimcik | Poisson Sigma Models and Manin Pairs |