Exact Solution of the One-Dimensional Non-Abelian Coulomb Gas at Large N

TL;DR

This paper provides an exact large N solution for a one-dimensional non-Abelian Coulomb gas, revealing a first-order phase transition and connecting to two-dimensional adjoint QCD with heavy matter fields.

Contribution

It offers the first explicit large N solution for the thermodynamics of a one-dimensional non-Abelian Coulomb gas, including phase transition analysis.

Findings

Identifies a first-order confinement-deconfinement phase transition.

Provides explicit thermodynamic properties of the system.

Connects the model to two-dimensional adjoint QCD with large matter masses.

Abstract

The problem of computing the thermodynamic properties of a one-dimensional gas of particles which transform in the adjoint representation of the gauge group and interact through non-Abelian electric fields is formulated and solved in the large $N$ limit. The explicit solution exhibits a first order confinement-deconfinement phase transition with computable properties and describes two dimensional adjoint QCD in the limit where matter field masses are large.