Space-Time Geometry of Three-Dimensional Yang-Mills Theory

TL;DR

This paper reformulates 3D $SU(2)$ Yang-Mills theory as a gravity-like theory using gauge-invariant variables, revealing new equations derived from a torsion-square action, thus providing a novel geometric perspective.

Contribution

It introduces a complete reformulation of 3D Yang-Mills theory as a gravity-like model in Riemann-Cartan space-time with gauge-invariant variables.

Findings

Yang-Mills equations derived from a torsion-square action

Reformulation as a gravity-like theory in Riemann-Cartan space

Complete gauge-invariant variable description

Abstract

It is shown that the $SU(2)$ Yang-Mills theory in $3$-dimensional Riemann-Cartan space-time can be completely reformulated as a gravity-like theory in terms of gauge invariant variables. The resulting Yang-Mills induced equations are found, and it is demonstrated that they can be derived from a torsion-square type of action.