Absence of higher order corrections to the non-Abelian topological mass term

TL;DR

This paper proves that in non-Abelian Yang-Mills-Chern-Simons theory, the Chern-Simons coefficient remains uncorrected beyond one loop in axial gauge, extending the Coleman-Hill result to non-Abelian cases.

Contribution

It demonstrates that the non-Abelian Chern-Simons coefficient does not receive higher-order quantum corrections beyond one loop in axial gauge, generalizing the Coleman-Hill theorem.

Findings

Chern-Simons coefficient is gauge dependent but physically meaningful in axial gauge.

No quantum correction beyond one loop to the Chern-Simons coefficient in axial gauge.

The ratio 4πm/g² remains unrenormalized beyond one loop in infrared safe gauges.

Abstract

We study the Yang-Mills-Chern-Simons theory systematically in an effort to generalize the Coleman-Hill result to the non-Abelian case. We show that, while the Chern-Simons coefficient is in general gauge dependent in a non-Abelian theory, it takes on a physical meaning in the axial gauge. Using the non-Abelian Ward identities as well as the analyticity of the amplitudes in the momentum variables, we show that, in the axial gauge, the Chern-Simons coefficient does not receive any quantum correction beyond one loop. This allows us to deduce that the ratio ${4\pi m\over g^{2}}$ is unrenormalized, in a non-Abelian theory, beyond one loop in any infrared safe gauge. This is the appropriate generalization of the Coleman-Hill result to non-Abelian theories. Various other interesting properties of the theory are also discussed.