Yang-Mills Theory In Axial Gauge

TL;DR

This paper studies the Yang-Mills functional integral in an axial gauge, resolving Gauss's law to describe the theory with fewer variables and demonstrating an area law for the Wilson loop, relevant for infrared behavior.

Contribution

It introduces a simplified formulation of Yang-Mills theory in axial gauge with fewer variables and computes the Wilson loop showing an area law.

Findings

Resolved Gauss's law in axial gauge reduces variables by half.

Derived an effective description involving a field in the Cartan subgroup.

Calculated Wilson loop exhibiting an area law, indicating confinement.

Abstract

The Yang-Mills functional integral is studied in an axial variant of 't Hooft's maximal Abelian gauge. In this gauge Gau\ss ' law can be completely resolved resulting in a description in terms of unconstrained variables. Compared to previous work along this line starting with work of Goldstone and Jackiw one ends up here with half as many integration variables, besides a field living in the Cartan subgroup of the gauge group and in D-1 dimension. The latter is of particular relevance for the infrared behaviour of the theory. Keeping only this variable we calculate the Wilson loop and find an area law.