Adjoint non-Abelian Coulomb gas at large N

TL;DR

This paper analyzes a non-Abelian Coulomb gas model, solving it in the large N limit to reveal a first order phase transition and connecting it to 1+1-dimensional QCD with heavy adjoint matter.

Contribution

It provides an explicit large N solution of the non-Abelian Coulomb gas and links it to lower-dimensional QCD models.

Findings

First order confinement-deconfinement phase transition identified.

Explicit solution for adjoint charges in the large N limit.

Continuum limit describes 1+1-dimensional QCD with heavy adjoint matter.

Abstract

The non-Abelian analog of the classical Coulomb gas is discussed. The statistical mechanics of arrays of classical particles which transform under various representations of a non-Abelian gauge group and which interact through non-Abelian electric fields are considered. The problem is formulated on the lattice and, for the case of adjoint charges, it is solved in the large N limit. The explicit solution exhibits a first order confinement-de-confinement phase transition with computable properties. In one dimension, the solution has a continuum limit which describes 1+1-dimensional quantum chromodynamics (QCD) with heavy adjoint matter.