Dreibein as prepotential for three-dimensional Yang-Mills theory

TL;DR

This paper proposes using the dreibein as a prepotential in three-dimensional SO(3) Yang-Mills theory, offering a gauge-invariant metric and a new perspective on monopole configurations and topological features.

Contribution

It introduces the dreibein as a gauge transformation homogenous prepotential, linking the metric to gauge invariance and topological monopole solutions in 3D Yang-Mills theory.

Findings

Dreibein transforms homogeneously under gauge transformations.

The metric derived from the dreibein is gauge invariant.

Topologically non-trivial monopoles correspond to conformally flat metrics.

Abstract

We advocate and develop the use of the dreibein (and the metric) as prepotential for three-dimensional SO(3) Yang-Mills theory. Since the dreibein transforms homogeneously under gauge transformation, the metric is gauge invariant. For a generic gauge potential, there is a unique dreibein on fixing the boundary condition. Topologically non-trivial monopole configurations are given by conformally flat metrics, with scalar fields capturing the monopole centres. Our approach also provides an ansatz for the gauge potential covering the topological aspects.