Renormalization Group Study of Chern-Simons Field Coupled to Scalar Matter in a Modified BPHZ Subtraction Scheme

TL;DR

This paper employs a modified BPHZ subtraction scheme to compute two-loop renormalization group functions for a Chern-Simons field coupled to scalar matter, providing insights into quantum corrections in this gauge theory.

Contribution

It introduces a soft BPHZ subtraction method for two-loop calculations in Chern-Simons scalar theories, offering a novel approach to renormalization.

Findings

Calculated two-loop RG functions for the model.

Compared results with existing literature.

Validated the modified subtraction scheme.

Abstract

We apply a soft version of the BPHZ subtraction scheme to the computation of two-loop corrections from an Abelian Chern-Simons field coupled to (massive) scalar matter with a $\lambda(\Phi^\dag\Phi)^2$ and $\nu(\Phi^\dag\Phi)^3$ self-interactions. The two-loop renormalization group functions are calculated. We compare our results with those in the literature.