Differential Regularization of Topologically Massive Yang-Mills Theory and Chern-Simons Theory

TL;DR

This paper uses differential renormalization to analyze three-dimensional topologically massive Yang-Mills and Chern-Simons theories, simplifying calculations and confirming known parameter shifts.

Contribution

It applies differential renormalization to these theories, providing explicit one-loop calculations and clarifying the relationship between massive Yang-Mills and Chern-Simons theories.

Findings

Computed one-loop propagators and vertices.

Derived the one-loop local effective action.

Confirmed the shift in the Chern-Simons level parameter.

Abstract

We apply differential renormalization method to the study of three-dimensional topologically massive Yang-Mills and Chern-Simons theories. The method is especially suitable for such theories as it avoids the need for dimensional continuation of three-dimensional antisymmetric tensor and the Feynman rules for three-dimensional theories in coordinate space are relatively simple. The calculus involved is still lengthy but not as difficult as other existing methods of calculation. We compute one-loop propagators and vertices and derive the one-loop local effective action for topologically massive Yang-Mills theory. We then consider Chern-Simons field theory as the large mass limit of topologically massive Yang-Mills theory and show that this leads to the famous shift in the parameter $k$. Some useful formulas for the calculus of differential renormalization of three-dimensional field theories are given in an Appendix.