Quark Confinement and Dual Representation in 2+1 Dimensional Pure Yang-Mills Theory

TL;DR

This paper investigates quark confinement in 2+1 dimensional pure Yang-Mills theory by employing instanton methods, revealing a dynamically generated mass gap and a dual representation involving monopoles and the Sine-Gordon field.

Contribution

It introduces a stable monopole configuration dressed by mean field effects and demonstrates the dynamical generation of a mass gap using non-perturbative Coulomb gas results.

Findings

Mass gap is dynamically generated in the gauge theory.

Stable monopole configurations are identified.

Disorder operator is expressed via the Sine-Gordon field.

Abstract

We study the quark confinement problem in 2+1 dimensional pure Yang-Mills theory using euclidean instanton methods. The instantons are regularized and dressed Wu-Yang monopoles. The dressing of a monopole is due to the mean field of the rest of the monopoles. We argue that such configurations are stable to small perturbations unlike the case of singular, undressed monopoles. Using exact non-perturbative results for the 3-dim. Coulomb gas, where Debye screening holds for arbitrarily low temperatures, we show in a self-consistent way that a mass gap is dynamically generated in the gauge theory. The mass gap also determines the size of the monopoles. In a sense the pure Yang-Mills theory generates a dynamical Higgs effect. We also identify the disorder operator of the model in terms of the Sine-Gordon field of the Coulomb gas.