Two-dimensional QCD on the sphere and on the cylinder

Abstract

The partition functions of QCD2 on simple surfaces admit representations in terms of exponentials of the inverse coupling, that are modular transforms of the usual character expansions. We review the construction of such a representation in the case of the cylinder, and show how it leads to a formulation of QCD2 as a $c=1$ matrix model of the Kazakov-Migdal type. The eigenvalues describe the positions of $N$ Sutherland fermions on a circle, while their discretized momenta label the representations in the corresponding character expansion. Using this language, we derive some new results: we give an alternative description of the Douglas-Kazakov phase transition on the sphere, and we argue that an analogous phase transition exists on the cylinder. We calculate the large $N$ limit of the partition function on the cylinder with boundary conditions given by semicircular distributions of eigenvalues, and we find an explicit expression for the large $N$ limit of the Itzykson-Zuber integral with the same boundary conditions. (Talk given at the ``Workshop on high energy physics and cosmology'' at Trieste, July 1993.)

12 pages, plain latex, DFTT 50/93

References in corpus (1)

• Conformal Field Theory Techniques for Large N Group Theory

Cited by in corpus (13)

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• Instanton contributions to Wilson loops with general winding number in two dimensions and the spectral density
• The instanton contributions to Yang-Mills theory on the torus: localization, Wilson loops and the perturbative expansion
• Two-dimensional gauge theories of the symmetric group S_n in the large-n limit
• Two-dimensional Yang-Mills theory: perturbative and instanton contributions, and its relation to QCD in higher dimensions
• Two-dimensional QCD and instanton contribution
• Large-N limit of the generalized 2D Yang-Mills theory on cylinder
• Wilson loops in the adjoint representation and multiple vacua in two-dimensional Yang-Mills theory
• A new large N phase transition in YM2
• Eigenvalue Dynamics and the Matrix Chain
• Topological contributions in two-dimensional Yang-Mills theory: from group averages to integration over algebras