Vacuum Structure of Two-Dimensional Gauge Theories for Arbitrary Lie Groups

Abstract

Using the well established machinery of Wilson loop calculations we investigate the multiple vacua of two dimensional Yang-Mills theories with infinitely massive adjoint matter. In particular, via group theoretical techniques we calculate string tensions between charges and find the number of vacua for each compact Lie symmetry group. The counting of vacua is in agreement with the standard classification based on the topology of the effective gauge group $π_1(G/Z)$ when one considers arbitrary numbers of adjoint charges in the system. For systems with limited numbers of charges we find additional "meta-stable" vacuum states. Finally we discuss t'Hooft's disorder operators in this setting as number operators for the multiple vacua.