Radiative Corrections in Nonrelativistic Chern-Simons Theory

TL;DR

This paper calculates the one-loop effective potential for supersymmetric and non-Abelian Chern-Simons theories, including radiative effects, demonstrating regularization scheme independence in different gauge choices.

Contribution

It provides the first detailed one-loop effective potential calculations for nonrelativistic supersymmetric and non-Abelian Chern-Simons matter theories with gauge background effects.

Findings

Effective potentials computed in multiple gauges.

Results are regularization scheme independent.

Radiative effects from background gauge fields included.

Abstract

We present the one-loop scalar field effective potential for the $N=2$ supersymmetric nonrelativistic self-interacting matter fields coupled to an Abelian Chern-Simons gauge field and for its generalization when bosonic matter fields are coupled to non-Abelian Chern-Simons field. In both models, Gauss's law linearly relates the magnetic field to the matter field densities; hence, we also include radiative effects from the background gauge field. We compute the scalar field effective potentials in two gauge families, a gauge reminiscent of the $R_\xi$-gauge in the limit $\xi\rightarrow 0$ and in the Coulomb family gauges. We regularize the theory with operator regularization and a cutoff to demonstrate that the results are independent of the regularization scheme.