Third Workshop on Nonperturbative Aspects of Gauge
Fields and Strings
Jena, February 22 - 24, 2001
Twenty-eight 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 at 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 seems rather hopeless at present. 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 or, more generally, bulk/boundary correspondence. Gravity theories in D+1 dimensions, stemming from the low energy expansion of string theory, are conjectured to be equivalent to a D-dimensional Yang-Mills theory on its boundary. In this way one hopes to gain insight into the strong coupling regime of the respective gauge theory, not accessible to standard perturbation theory. In particular, using effective supergravity models, one can study the large-N sector of gauge theories, Wilson loops, glueballs and even the shape of the flux tube. In order to tie in to more realistic gauge theories such as four-dimensional QCD, it is of interest to study more general gauged supergravity backgrounds.
There is also another recent impact of string theory on standard Yang-Mills theory: string vacua with a nonvanishing B-field have been seen to induce a noncommutative deformation of the space-time structure underlying effective Yang-Mills theories on branes. This has revived older ideas of Connes and others to define and study gauge theories on noncommutative spacetimes. To some extent, such gauge theories may be viewed as regularizations of continuum Yang-Mills theory, providing an alternative to the standard lattice approach.
It thus seems that, after a long period of divergence, gauge field theory, gravity and string theory are again converging towards each other. It is the purpose of the workshop to bring together experts from several ends of the activities described above, allowing for mutual inspiration and lively interaction.
