Non-Renormalization Properties of the Chern-Simons Action Coupled to Matter

TL;DR

This paper demonstrates that in a 3D abelian gauge model with massless scalar matter, the Chern-Simons term remains uncorrected by quantum effects, ensuring its non-renormalization within a specific renormalization scheme.

Contribution

It establishes the non-renormalization of the Chern-Simons term in a matter-coupled abelian gauge theory using Ward identities and the BPHZL scheme.

Findings

Chern-Simons term has no radiative corrections

The beta function for the Chern-Simons coupling vanishes

Trace anomalies are controlled by a local dilatation Ward identity

Abstract

We analyze an abelian gauge model in 3 dimensions which includes massless scalar matter fields. By controlling the trace anomalies with a local dilatation Ward identity, we show that, in perturbation theory and within the BPHZL scheme, the Chern-Simons term has no radiative corrections. This implies, in particular, the vanishing of the corresponding $\beta$ function in the renormalization group equation.