Universalty and Ultraviolet Regularizations of Chern-Simons Theory

TL;DR

This paper investigates how different ultraviolet regularizations affect the radiative corrections to the gauge coupling in Chern-Simons theory, revealing three regimes with distinct shifts and universality properties, and suggesting links to conformal theories.

Contribution

It demonstrates the dependence of the gauge coupling shift on the ultraviolet behavior of scalar and pseudoscalar terms in a general regularization scheme, identifying three distinct regimes.

Findings

The coupling shift is $k+h^{\/vee}$ when scalar dominates.

The shift is $k+s h^{\/vee}$ with $s=0$ or $2$ when pseudoscalar dominates.

In the borderline case, the shift is arbitrary and regularization-dependent.

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.