Theta Sectors and Thermodynamics of a Classical Adjoint Gas

TL;DR

This paper explores how the topology of a 1+1 dimensional SU(N) gauge field system influences the thermodynamics of an adjoint gas, revealing multiple vacua and pressure-dependent behaviors.

Contribution

It explicitly demonstrates the existence of multiple vacua parameterized by a superselection variable and analyzes the equation of state across different pressure regimes.

Findings

Multiple vacua exist, labeled by k=1,...,N.

At low pressure, the equation of state depends non-trivially on k.

At high pressure, screening makes the equation of state independent of k.

Abstract

The effect of topology on the thermodynamics of a gas of adjoint representation charges interacting via 1+1 dimensional SU(N) gauge fields is investigated. We demonstrate explicitly the existence of multiple vacua parameterized by the discrete superselection variable k=1,...,N. In the low pressure limit, the k dependence of the adjoint gas equation of state is calculated and shown to be non-trivial. Conversely, in the limit of high system pressure, screening by the adjoint charges results in an equation of state independent of k. Additionally, the relation of this model to adjoint QCD at finite temperature in two dimensions and the limit of large N are discussed.