The stability of vacua in two-dimensional gauge theory

TL;DR

This paper analyzes the stability of vacua in two-dimensional gauge theories across various gauge groups, using Wilson lines and representation theory to identify stable vacua against heavy matter pair production.

Contribution

It provides a general method to determine vacuum stability in 2D gauge theories using Wilson loop correlators and Lie group representation theory.

Findings

Identifies stable vacua for different gauge groups.

Reduces stability problem to Lie group representation theory.

Provides a comprehensive solution applicable to all simple, simply connected gauge groups.

Abstract

We discuss the stability of vacua in two-dimensional gauge theory for any simple, simply connected gauge group. Making use of the representation of a vacuum in terms of a Wilson line at infinity, we determine which vacua are stable against pair production of heavy matter in the adjoint of the gauge group. By calculating correlators of Wilson loops, we reduce the problem to a problem in representation theory of Lie groups, that we solve in full generality.