Renormalization Ambiguities and Gauge Symmetry in Chern–simons Theories

Abstract

The universality of radiative corrections to the gauge coupling constant k of the ChernSimons theory is studied in a very general regularization scheme in the background gauge formalism. The effective coupling constant k eff induced by radiative corrections can be any real number depending on the balance between the ultraviolet behavior of scalar and pseudoscalar terms in the regularized action. This ambiguity of the effective action is related to the ambiguity in the parity anomaly of three-dimensional Dirac fermions. The effective action also contains a non-analytic term in the gauge field with the same coefficient and opposite gauge transformation in such a way that the effective action is gauge-invariant. The results open the possibility of a connection with non-rational two-dimensional conformal theories for non-integer values of k eff .