Dual gluons and monopoles in 2+1 dimensional Yang-Mills theory

TL;DR

This paper reinterprets 2+1D Yang-Mills theory using 3-manifold metrics, linking dual gluons to diffeomorphisms and monopoles to Ricci tensor degeneracies, suggesting a mechanism for gluon mass and confinement.

Contribution

It introduces a novel geometric framework connecting dual gluons and monopoles in 2+1D Yang-Mills theory, proposing a new approach to understanding confinement.

Findings

Dual gluons relate to 3-manifold diffeomorphisms

Monopoles correspond to Ricci tensor degeneracies

Interaction between dual gluons and monopoles implies gluon mass

Abstract

2+1-dimensional Yang-Mills theory is reinterpreted in terms of metrics on 3-manifolds. The dual gluons are related to diffeomorphisms of the 3-manifold. Monopoles are identified with points where the Ricci tensor has triply degenerate eigenvalues. The dual gluons have the desired interaction with these monopoles. This would give a mass for the dual gluons resulting in confinement.