Yang-Mills theory, 2+1 and 3+1 dimensions

TL;DR

This paper reviews the analysis of (2+1)-dimensional Yang-Mills theory using gauge-invariant variables, discussing key physical quantities and potential extensions to 3+1 dimensions.

Contribution

It provides a comprehensive review of gauge-invariant matrix variable methods applied to Yang-Mills theory in lower dimensions and explores possible extensions to higher dimensions.

Findings

Analysis of vacuum wavefunction and string tension in YM_{2+1}

Relation between gluon propagator mass and magnetic mass at finite temperature

Discussion of extending methods to 3+1 dimensions

Abstract

I review the analysis of (2+1)-dimensional Yang-Mills ($YM_{2+1})$ theory via the use of gauge-invariant matrix variables. The vacuum wavefunction, string tension, the propagator mass for gluons, its relation to the magnetic mass for $YM_{3+1}$ at nonzero temperature and the extension of our analysis to the Yang-Mills-Chern-Simons theory are discussed. A possible extension to 3+1 dimensions is also briefly considered.