Large N Gauge Theory -- Expansions and Transitions

Abstract

We use solvable two-dimensional gauge theories to illustrate the issues in relating large N gauge theory to string theory. We also give an introduction to recent mathematical work which allows constructing master fields for higher dimensional large N theories. We illustrate this with a new derivation of the Hopf equation governing the evolution of the spectral density in matrix quantum mechanics. Based on lectures given at the 1994 Trieste Spring School on String Theory, Gauge Theory and Quantum Gravity.

RU-94-72 (LaTeX with espcrc2.sty and epsf.sty, 26 pp., 6 figures. References added and other improvements.)

References in corpus (11)

• Two Dimensional Gauge Theories Revisited
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• Infinite Symmetry in the Quantum Hall Effect
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• On the Large N Limit of the Itzykson-Zuber Integral
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Cited by in corpus (18)

• SU(N) gauge theories at large N
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• Nonhermitean Random Matrix Models
• Introductory lectures to large-N QCD phenomenology and lattice results
• Large N_c confinement and turbulence
• Volume dependence of two-dimensional large-N QCD with a nonzero density of baryons
• Beyond islands: A free probabilistic approach
• The Algebras of Large N Matrix Mechanics
• The generalized master fields
• Solving loop equations by Hitchin systems via holography in large-N QCD_4
• The phase diagram of $T\bar{T}$-deformed Yang-Mills theory on the sphere
• Collective potential for large N hamiltonian matrix models and free Fisher information
• Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
• Exact beta function from the holographic loop equation of large-N QCD_4
• Non-anomalous `Ward' identities to supplement large-N multi-matrix loop equations for correlations
• Crossover in densities of confined particles with finite range of interaction
• Yang-Mills mass gap at large-N, non-commutative YM theory, topological quantum field theory and hyperfiniteness
• Twisted local systems solve the (holographic) loop equation of large-N QCD_4