Adjoint non-Abelian Coulomb gas at large N

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.

21 pages, LaTex

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• One-dimensional classical adjoint SU(2) Coulomb Gas
• Order Parameter for Confinement in Large N Gauge Theories with Fundamental Matter
• Theta Sectors and Thermodynamics of a Classical Adjoint Gas