Chern-Simons vs. Yang-Mills gaugings in three dimensions

TL;DR

This paper shows that in three-dimensional supergravity, Yang-Mills gaugings can be reformulated as equivalent Chern-Simons gaugings with non-semisimple gauge groups, unifying different approaches.

Contribution

It proves the on-shell equivalence between Yang-Mills and Chern-Simons gaugings in three dimensions, including cases with massive vectors and non-semisimple groups.

Findings

Yang-Mills gaugings are equivalent to Chern-Simons gaugings with non-semisimple groups

The equivalence holds on-shell for theories with semisimple gauge groups

Several explicit examples illustrate the theoretical results

Abstract

Recently, gauged supergravities in three dimensions with Yang-Mills and Chern-Simons type interactions have been constructed. In this article, we demonstrate that any gauging of Yang-Mills type with semisimple gauge group G_0, possibly including extra couplings to massive Chern-Simons vectors, is equivalent on-shell to a pure Chern-Simons type gauging with non-semisimple gauge group $G_0 \ltimes T \subset G$, where T is a certain translation group, and where G is the maximal global symmetry group of the ungauged theory. We discuss several examples.