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

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 that is both Becchi-Rouet-Stora (BRS) invariant and Landau supersymmetric and an effective action that is 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 $k\to k+c_V$ of the bare Chern-Simons parameter $k$ in connection 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.