B. Bringoltz
University of Washington
barak@phys.washington.edu
M. Shifman
University of Minnesota
shifman@umn.edu
M. Unsal
Stanford University
unsal@slac.stanford.edu
L. Yaffe
University of Washington
yaffe@phys.washington.edu
Program Coordinator:
Laura Lee
lee@phys.washington.edu
(206) 685-3509
Application form
February 3 - 6, 2009
For many years it has been understood that non-Abelian gauge theories simplify in the limit of large N : sending N to infinity is a type of classical limit. Although we are still far from having exact solutions for interesting theories, much insight has been gained from considering gauge theory dynamics in the large N limit. Recently there have been noteworthy theoretical and phenomenological developments which are contributing to our understanding of non-perturbative gauge theory dynamics in four dimensions.
These include explorations of the rich network of exact relations which link the large N limits of different theories, significant results from numerical studies of higher rank gauge theories, phenomenological large-N studies of baryons and of QCD thermodynamics, and studies of deformations and compactifications of gauge theories, including chiral theories, for which one can gain analytic control over non-perturbative phenomena.
We believe that a workshop on recent developments in large N gauge theories would be quite timely and would help stimulate continuing developments in this area.
Many different non-perturbative large N equivalences, relating theories with different gauge groups and matter content, are now known to hold provided appropriate symmetry realization conditions are satisfied. These include many examples associated with orbifold (or orientifold) projections, some of which relate supersymmetric theories to non-supersymmetric QCD-like theories. A variety of novel predictions for real QCD have been obtained in this fashion. Large N volume independence is another type of large N equivalence generated by an orbifold projection. Volume independence exactly relates large N properties of a wide class of QCD-like theories on "Eguchi-Kawai" reduction, relating a large N lattice gauge theory to a single-site matrix model, is a special case of such volume independence. The original version of Eguchi-Kawai reduction (as well as "twisted" and "quenched" variants) fails for sufficiently weak coupling due to unwanted symmetry breaking. But examples of QCD-like theories which do satisfy complete volume independence are now known. Large N orientifold equivalence and volume independence may be combined to produce a fully reduced version of a large N generalization of QCD with light fermions. Lattice studies of the resulting reduced models should be possible and will allow one to extract infinite volume physics from simulations with only a single site. Lattice simulations at larger-N Recent numerical studies of SU(N) gauge theories with N ranging up to about 10 (on large lattices), and much larger on small lattices, have yielded results on the N dependence of string tensions, deconfinement temperature, domain wall tensions, bulk and finite volume phase transitions, spectral properties of Wilson loops, meson spectra, theta dependence, and other properties. Most importantly, these studies have shown that, for many important quantities, the N dependence is remarkably smooth from large values of N all the way down to N = 3. Simulations in the near future should be able to study a wider variety of interesting large N theories including supersymmetric theories, theories related by orbifold projections, and reduced models with dynamical fermions. Our current knowledge of the four dimensional chiral gauge theories remains at a rudimentary level. To date, there is no controllable dynamical framework to study non-Abelian strongly coupled chiral gauge theory dynamics. This is a deplorable situation considering the potential phenomenological relevance of such theories to TeV scale physics. Any progress in this area must involve novel techniques and understanding of non-perturbative dynamics. It has recently been noted that the center-stabilizing double trace deformations mentioned above can provide a useful analytical tool for chiral gauge theories. In some cases one finds (as in the pure Yang-Mills case) an analytically tractable regime when the theory is compactified on S1 × R3 , with physics which is smoothly connected to the decompactified limit. Large-N phenomenology The prime motivation for theoretical studies of large-N gauge theories is to improve our non-perturbative understanding of 'low/moderate'-N physical gauge theories such as QCD. This can be accomplished in a phenomenological framework where one uses the aforementioned theoretical features of large-N theories (e.g. factorization of correlation functions, volume/temperature independence, suppression of fundamental fermions, orientifold projections, simplification of baryon structure etc.) to make qualitative and quantitative predictions in physically relevant cases. This phenomenological approach has been recently applied to several areas of research that, in addition to those mentioned in the above sections, include various properties of the QCD baryon sector, the thermodynamics of QCD at nonzero temperature and density, and chiral dynamics.
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