Renormalization Ambiguities in Chern-Simons Theory

TL;DR

This paper introduces a new family of gauge invariant regularizations for Chern-Simons theories, revealing an ambiguity in one-loop renormalization of the coupling constant that parallels known anomalies.

Contribution

It presents a novel class of gauge invariant regularizations that produce arbitrary integer shifts in the coupling constant, highlighting a new ambiguity in quantum corrections.

Findings

Regularizations generate shifts of the form k→k+2sc_v with arbitrary integer s.

An explicit regularization case with no radiative correction to the coupling constant.

The ambiguity relates to the parity anomaly in (2+1) fermionic theories.

Abstract

We introduce a new family of gauge invariant regularizations of Chern-Simons theories which generate one-loop renormalizations of the coupling constant of the form $k\to k+2 s c_v$ where $s$ can take any arbitrary integer value. In the particular case $s=0$ we get an explicit example of a gauge invariant regularization which does not generate radiative corrections to the bare coupling constant. This ambiguity in the radiative corrections to $k$ is reminiscent of the Coste-L\"uscher results for the parity anomaly in (2+1) fermionic effective actions.