Confinement in (2+1)-Dimensional Gauge Theories at Weak Coupling

TL;DR

This paper explores the weak coupling regime of (2+1)-dimensional SU(N) Yang-Mills theory in axial gauge, revealing its equivalence to integrable (1+1)-dimensional models and enabling analysis of static potentials and spectral features.

Contribution

It demonstrates the equivalence of (2+1)D SU(N) Yang-Mills theory to integrable (1+1)D models in axial gauge, providing new insights into static potentials and spectrum at weak coupling.

Findings

Determined static charge potentials at weak coupling.

Identified spectral features through integrable model equivalence.

Clarified the role of non-local couplings in the theory.

Abstract

In axial gauge, the (2+1)-dimensional SU($N$) Yang-Mills theory is equivalent to a set of (1+1)-dimensional integrable models with a non-local coupling between charge densities. This fact makes it possible to determine the static potential between charges at weak coupling in an anisotropic version of the theory, and understand features of the spectrum.