Yang-Mills as massive Chern-Simons theory: a third way to three-dimensional gauge theories

TL;DR

This paper introduces a novel modification of three-dimensional Yang-Mills theory that includes a parity-preserving interaction term, which cannot be derived from a gauge-invariant local action, using a 'third way' approach inspired by massive gravity.

Contribution

It proposes a new way to modify 3D Yang-Mills equations through a non-Lagrangian interaction term, expanding the understanding of gauge theories in three dimensions.

Findings

The modified YM equation is not derived from a local gauge-invariant action.

Consistency is achieved via a 'third way' similar to minimal massive gravity.

Connections are made to the 'novel Higgs mechanism' in Chern-Simons theories.

Abstract

The Yang-Mills (YM) equation in three spacetime dimensions (3D) can be modified to include a novel parity-preserving interaction term, with inverse mass parameter, in addition to a possible topological mass term. The novelty is that the modified YM equation is not the Euler-Lagrange equation of any gauge-invariant local action for the YM gauge potential alone. Instead, consistency is achieved in the "third way" exploited by 3D "minimal massive gravity". We relate our results to the "novel Higgs mechanism" for Chern-Simons gauge theories.