Mass Gap and Confinement in (2+1)-Dimensional Yang-Mills Theory

TL;DR

This paper analyzes the origin of the mass gap in (2+1)-dimensional Yang-Mills theory using gauge-invariant methods, deriving an analytical vacuum wavefunction and calculating the string tension that matches lattice simulations.

Contribution

It introduces a gauge-invariant matrix parametrization to analytically derive the vacuum wavefunction and string tension in (2+1)-D Yang-Mills theory, confirming results with simulations.

Findings

Mass gap is explained via gauge-invariant analysis.

Derived an analytical expression for the vacuum wavefunction.

Calculated string tension agrees with lattice Monte Carlo results.

Abstract

Using a gauge-invariant matrix parametrization of the gauge fields, we present an analysis of how the mass gap arises in (2+1)-dimensional Yang-Mills theory. We further derive an analytical continuum expression for the vacuum wavefunction and based on this we calculate the string tension which is in excellent agreement with Monte Carlo simulations of the corresponding lattice gauge theory.