Universalty and Ultraviolet Regularizations of Chern-Simons Theory

Abstract

The universality of radiative corrections to the gauge coupling constant $k$ of Chern-Simons theory is studied in a very general regularization scheme. We show that the effective coupling constant $k$ induced by radiative corrections depends crucially on the balance between the ultraviolet behavior of scalar and pseudoscalar terms in the regularized action. There are three different regimes. When the ultraviolet leading term is scalar the coupling $k$ is shifted to $k+h^{\vee}$.However, if the leading term is pseudoscalar the shift is $k+s h^{\vee}$ with $s=0$ or $s=2$ depending on the sign of such a term. In the borderline case when the scalar and pseudoscalar terms have the same ultraviolet behavior the shift of $k$ becomes arbitrary (even non-integer) and depends on the parameters of the regularization. We also show that the coefficient of the induced gravitational Chern-Simons term is different for the three regimes and has the same universality properties than the effective coupling constant $k$. The results open the possibility of a connection with non-rational two-dimensional conformal theories in the borderline regime.