Physically meaningful and not so meaningful symmetries in Chern-Simons theory

TL;DR

This paper demonstrates that the Landau gauge supersymmetry in Chern-Simons theory is physically insignificant and explores the implications of this for the shift in the Chern-Simons level parameter, using BRS invariant regularization.

Contribution

It clarifies the non-physical nature of Landau gauge supersymmetry in Chern-Simons theory and analyzes the level shift using BRS invariant regulators.

Findings

Landau gauge supersymmetry has no physical significance in Chern-Simons theory.

The level shift $k o k+ ext{constant}$ is regulator-independent.

BRS invariant regulators yield consistent level shift results.

Abstract

We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action both BRS invariant and Landau supersymmetric and an effective action only BRS invariant is a finite field redefinition. Having established this, we use a BRS invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift $k \to k+\cv$ of the bare Chern-Simons parameter $k$ in conncection with the Landau supersymmetry. Finally, to convince ourselves that the shift above is not an accident of our regularization method, we comment on the fact that all BRS invariant regulators used as yet yield the same value for the shift.