The universality of the shift of the Chern-Simons parameter for a general class of BRS invariant regularizations

TL;DR

This paper demonstrates that the shift in the Chern-Simons parameter k is universal across a broad class of BRS invariant regularizations in SU(N) Chern-Simons theory, regardless of specific regularization parameters.

Contribution

It proves the universality of the k-shift in SU(N) Chern-Simons theory for a wide family of BRS invariant regularizations.

Findings

The shift k→k+sign(k)N occurs universally.

The shift is independent of regularization parameters.

Supports the conjecture of universality of the k-shift.

Abstract

We consider a biparametric family of BRS invariant regularization methods of SU(N) Chern-Simons theory (the parameters defining the family taking arbitrary values in $\RR^2$) and show that the shift $k\to k + sign(k) N$ of the Chern-Simons parameter $k$ occurs for arbitrary values of the family defining parameters. This supports irrefutably the conjecture that the shift of $k$ is universal for BRS invariant regulators.