Gauge-invariant formulation of the d=3 Yang-Mills theory

TL;DR

This paper reformulates 3D Yang-Mills theory using gauge-invariant variables related to a dual curved space, revealing a natural mechanism for mass gap generation and connecting Wilson loops to gravitational holonomy.

Contribution

It introduces a gauge-invariant metric tensor formulation of 3D Yang-Mills theory, linking Wilson loops to gravitational holonomy and proposing a new mass gap mechanism.

Findings

Reformulation of Yang-Mills in terms of metric tensor variables

Wilson loop expressed as gravitational holonomy

Identification of glueball fields with external coordinates

Abstract

We write down the Yang-Mills partition function and the average Wilson loop in terms of local gauge-invariant variables being the six components of the metric tensor of dual space. The Wilson loop becomes the trace of the parallel transporter in curved space, else called the gravitational holonomy. We show that the external coordinates mapping the 3d curved space into a flat 6d space play the role of glueball fields, and there is a natural mechanism for the mass gap generation.