The Chern-Simons Coefficient in the Higgs Phase

TL;DR

This paper investigates one-loop quantum corrections to the Chern-Simons coefficient in abelian Higgs models with supersymmetry, revealing quantized corrections and phase-dependent behaviors, with implications for nonabelian theories.

Contribution

It provides a detailed analysis of one-loop corrections to the Chern-Simons coefficient in supersymmetric abelian Higgs systems, highlighting phase-dependent effects and potential parallels in nonabelian models.

Findings

One-loop corrections are quantized in units of 1/4π.

In N=3 supersymmetry, symmetric phase correction vanishes.

Asymmetric phase correction is proportional to κ/(2π|κ|).

Abstract

We study one-loop corrections to the Chern-Simons coefficient $\kappa$ in abelian self-dual Chern-Simons Higgs systems and their $N=2$ and $N=3$ supersymmetric generalizations in both symmetric and asymmetric phases. One-loop corrections to the Chern-Simons coefficient of these systems turn out to be integer multiples of $1/4\pi$ in both phases. Especially in the maximally supersymmetric $N=3$ case, the correction in symmetric phase vanishes and that in asymmetric phase is $\kappa/(2\pi |\kappa|)$. Our results suggest that nonabelian self-dual systems might enjoy similar features. We also discuss various issues arising from our results.