Absence of higher order corrections to the non-Abelian Chern-Simons coefficient

TL;DR

This paper proves that in non-Abelian Chern-Simons theories with a topological mass term, the Chern-Simons coefficient receives no higher-order quantum corrections beyond one loop, extending previous Abelian results.

Contribution

It generalizes the Coleman-Hill analysis to non-Abelian theories, showing the absence of higher-order corrections using gauge Ward identities and analyticity.

Findings

No corrections beyond one loop in pure Yang-Mills-Chern-Simons theory

Uses gauge Ward identities and analyticity to establish non-renormalization

Extends Abelian results to non-Abelian gauge theories

Abstract

We extend the Coleman-Hill analysis to non-Abelian Chern-Simons theories containing a tree level topological mass term. We show, in the case of a pure Yang-Mills-Chern-Simons theory, that there are no corrections to the coefficient of the Chern-Simons term beyond one loop in the axial gauge. Our arguments use constraints coming only from small gauge Ward identities as well as the analyticity of the amplitudes, much like the proof in the Abelian case. Some implications of this result are also discussed.