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 π2/2. We use this as a lemma to provide a direct transcription for 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 S2. 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 elsewhere in the literature.