A note on the third way consistent deformation of Yang-Mills theory

TL;DR

This paper explores a novel third way consistent deformation of three-dimensional Yang-Mills theory, revealing a dual formulation as a Chern-Simons gauged sigma model that simplifies coupling to matter and supergravity.

Contribution

It demonstrates a dualization of the third way consistent deformation, providing a natural action formulation and enabling straightforward matter and gravity coupling.

Findings

Dualization yields a Chern-Simons gauged sigma model

Coupling to matter and gravity is simplified in the dual formulation

Derived coupling to N=1 supergravity

Abstract

Three-dimensional Yang-Mills theory allows for a deformation quadratic in the field strengths which can not be integrated to a local action without auxiliary fields. Yet, its covariant divergence consistently vanishes after iterating the equation, realizing a spin-1 analogue of `minimal massive gravity', which has been dubbed `third way consistent'. In this note, we show that after dualization of the three-dimensional gauge fields, the model possesses a natural action as a Chern-Simons coupled gauged sigma model. In this dual formulation, coupling to matter and to gravity becomes straightforward. As a direct application, we derive the coupling of the model to N=1 supergravity.