Vacuum Structure and $\theta$ States of Adjoint QCD in Two Dimensions

TL;DR

This paper investigates the topological vacuum structure of two-dimensional SU(N) adjoint QCD, classifying multiple vacua by a quantum number k and analyzing their physical properties through string tension and potential calculations.

Contribution

It explicitly demonstrates the vacuum multiplicity equals N and introduces a classification of worlds by the integer k, analogous to the theta parameter in QCD.

Findings

Vacuum multiplicity is N for SU(N) gauge group.

Effective string tensions depend on the quantum number k.

Vacuum energy varies with k.

Abstract

We address the issue of topological angles in the context of two dimensional SU(N) Yang-Mills theory coupled to massive fermions in the adjoint representation. Classification of the resulting multiplicity of vacua is carried outin terms of asymptotic fundamental Wilson loops, or equivalently, charges at the boundary of the world. We explicitly demonstrate that the multiplicity of vacuum states is equal to N for SU(N) gauge group. Different worlds of the theory are classified by the integer number k=0,1,...N-1 (superselection rules) which plays an analogous role to the $\theta$ parameter in QCD. Via two completely independent approaches we study the physical properties of these unconnected worlds as a function of k. First, we apply the well known machinery of the loop calculus in order to calculate the effective string tensions in the theory as function of $k$. The second way of doing the same physics is the standard particle/field theoretic calculation for the binding potential of a pair of infinitely massive fermions. We also calculate the vacuum energy as function of k.