Statistical physics of dyons and quark confinement

TL;DR

This paper develops a semiclassical model of SU(N) Yang--Mills theory using an ensemble of interacting dyons, successfully reproducing key features of quark confinement and deconfinement consistent with lattice results.

Contribution

It introduces an exactly solvable 3d quantum field theory framework for dyons that captures confinement phenomena in non-Abelian gauge theories.

Findings

Reproduces the confinement-deconfinement transition criteria.

Matches the critical temperature with lattice data.

Demonstrates confinement in G(2) gauge group.

Abstract

We present a semiclassical approach to the SU(N) Yang--Mills theory whose partition function at nonzero temperatures is approximated by a saddle point -- an ensemble of an infinite number of interacting dyons of N kinds. The ensemble is governed by an exactly solvable 3d quantum field theory, allowing calculation of correlations functions relevant to confinement. We show that known criteria of confinement are satisfied in this semiclassical approximation: (i) the average Polyakov line is zero below some critical temperature, and nonzero above it, (ii) a quark-antiquark pair has linear rising potential energy, (iii) the average spatial Wilson loop falls off exponentially with the area, (iv) N^2 gluons are canceled out from the spectrum, (v) the critical deconfinement temperature is in good agreement with lattice data. Using the same approximation, we find confinement for the exceptional gauge group G(2) and a first-order deconfinement transition, also in agreement with lattice findings.