String Tensions and Representations in Anisotropic 2+1-Dimensional Weakly-Coupled Yang-Mills Theory

TL;DR

This paper analyzes the confining properties of anisotropic (2+1)-dimensional Yang-Mills theory, revealing a sine law for string tension in one direction and the non-confinement of adjoint sources.

Contribution

It demonstrates the behavior of string tensions and confinement features in anisotropic Yang-Mills theory with new analytical insights.

Findings

String tension in x^2-direction follows a sine law.

Static adjoint sources are not confined.

Confined phase features are characterized in anisotropic setting.

Abstract

In earlier papers we established quark confinement analytically in anisotropic $(2+1)$-dimensional Yang-Mills theory with two gauge coupling constants. Here we point out a few features of the confining phase. These are: 1) the string tension in the $x^{2}$-direction as a function of representation obeys a sine law, and 2) static adjoint sources are not confined.