Shift versus no-shift in local regularizations of Chern-Simons theory

TL;DR

This paper investigates a family of local, BRS-invariant regularizations for SU(N) Chern-Simons theory that do not alter the Chern-Simons parameter at one loop, contrasting with traditional shift behaviors.

Contribution

The authors introduce a new class of regularizations that preserve the Chern-Simons parameter without the typical one-loop shift, providing insights into regularization effects in gauge theories.

Findings

Regularizations do not shift the Chern-Simons parameter at one loop.

The regularizations are local, BRS-invariant, and higher covariant derivative.

This challenges the conventional understanding of parameter shifts in Chern-Simons theory.

Abstract

We consider a family of local BRS-invariant higher covariant derivative regularizations of $SU(N)$ Chern-Simons theory that do not shift the value of the Chern-Simons parameter $k$ to $k+\,{\rm sign}(k)\,\cv$ at one loop.