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

TL;DR

This paper reveals universal patterns in two-dimensional Yang-Mills theories at large N, demonstrating phase transitions and providing explicit calculations for different gauge groups on various surfaces.

Contribution

It establishes a universal functional form for large N partition functions and Wilson loops across different gauge groups and surfaces, and details phase transitions in U(N) QCD_2.

Findings

Universal form of partition functions and Wilson loops at large N

Identification of a third-order phase transition in U(N) QCD_2 on the projective plane

Explicit computation of Wilson loops for SO(N) and Sp(N) on the sphere

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 \pi^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.