Workshop on Nonperturbative Aspects of Gauge Fields and Strings: JENA 2000

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.

Topics to be Covered

• nontrivial topology: lattice vs. continuum
• nontrivial topology: instantons vs. monopoles vs. vortices ...
• gauge fixing: (Gribov) ambiguities and defects
• confinement at work: supersymmetric gauge theories
• from strings to Yang-Mills: AdS/CFT correspondence
• new string backgrounds: noncommutative geometry

Session I: Thursday, February 10th, Lecture Hall 2, Abbeanum, Fröbelstieg 1

Session II: Friday, February 11th, Lecture Hall 2, Abbeanum, Fröbelstieg 1

Session III: Friday, February 11th, Lecture Hall 2, Abbeanum, Fröbelstieg 1

Session IV: Saturday, February 12th, Lecture Hall 2, Abbeanum, Fröbelstieg 1