B. Bringoltz
University of Washington

M. Shifman
University of Minnesota

M. Unsal
Stanford University

L. Yaffe
University of Washington

Program Coordinator:
Laura Lee
(206) 685-3509

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New frontiers in large N gauge theories

February 3 - 6, 2009

Understanding the dynamics of strongly coupled Yang-Mills theories with various types of matter remains a challenging problem. Lattice gauge theory is useful for vector-like theories, but practical numerical techniques for studying chiral theories are lacking.

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.

We envision focusing on the following topics:

  • Non-perturbative large-N equivalences
  • Lattice simulations at larger-N
  • Strongly coupled chiral gauge theories
  • Large-N phenomenology

    "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.

    Instead of relying on dynamical fermions to provide stabilization of center symmetry, it has also been recently understood how to add double trace deformations to the Yang-Mills action in a manner which preserves large N equivalence with the original undeformed theory (on R4 ) while at the same time preventing center symmetry breaking in small volume, thereby ensuring complete validity of large N volume independence. When studied on sufficiently small S1 × R3 , these deformed theories also provide an analytically tractable example of confinement which does not involve elementary scalars or supersymmetry. There are strong reasons to believe that the properties of the deformed Yang-Mills theory (or a one flavor deformed QCD) on S1 × R3 are completely smooth as one decompactifies to R4 . These theories possess a rich assortment of topological excitations and it will be quite interesting to compare the small S1 semi-classical results with lattice simulations.

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    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.

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