Universal Aspects of Two-Dimensional Yang-Mills Theory at Large N

Abstract

We show that the large N partition functions and Wilson loop observables of two-dimensional Yang-Mills theories admit a universal functional form irrespective of the gauge group. We demonstrate that U(N) QCD_2 undergoes a large N, third-order phase transition on the projective plane at an area-coupling product of π^2/2. We use this as a lemma to provide a direct transcription of the partition functions and phase portraits of Yang-Mills theory from the U(N) on RP^2 at large N to the other classical Lie groups on S^2. We compute the expectation value of the Wilson loops in the fundamental representation for SO(N) and Sp(N) on the two sphere. Finally we compare the strong- and weak-coupling limit of these expressions with those found elswhere in the literature.

20 pages, plain TeX

References in corpus (3)

• Large N 2D Yang-Mills Theory and Topological String Theory
• Large $N$ Phases of Chiral QCD_2
• Counting Strings and Phase Transitions in 2D QCD

Cited by in corpus (4)

• Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
• Evaluation of the Free Energy of Two-Dimensional Yang-Mills Theory
• Field Strength Correlators For 2D Yang-Mills Over Riemann Surfaces
• Topology Change and theta-Vacua in 2D Yang-Mills Theory