Inconsistency of Naive Dimensional Regularizations and Quantum Correction to Non-Abelian Chern-Simons-Matter Theory Revisited

TL;DR

This paper examines the inconsistencies in common regularization methods for non-Abelian Chern-Simons theories and demonstrates that quantum corrections affect both the Chern-Simons coefficient and spinor fields when using a consistent regularization approach.

Contribution

It identifies issues with naive regularization methods and provides a revised analysis showing quantum corrections to both the Chern-Simons coefficient and spinor fields.

Findings

Naive dimensional regularization is inconsistent for Chern-Simons theories.

Quantum corrections modify the Chern-Simons coefficient.

Spinor fields also receive finite quantum corrections.

Abstract

We find the inconsistency of dimensional reduction and naive dimensional regularization in their applications to Chern-Simons type gauge theories. Further we adopt a consistent dimensional regularization to investigate the quantum correction to non-Abelian Chern-Simons term coupled with fermionic matter. Contrary to previous results, we find that not only the Chern-Simons coefficient receives quantum correction from spinor fields, but the spinor field also gets a finite quantum correction.