Integer Quantization of the Chern-Simons Coefficient in a Broken Phase

TL;DR

This paper investigates how the Chern-Simons coefficient behaves under renormalization in a spontaneously broken nonabelian gauge theory, demonstrating that the quantization condition remains intact despite quantum corrections.

Contribution

It shows that in a broken phase, the ratio of the Chern-Simons coupling to the gauge coupling is shifted by a quantized amount, preserving the integer quantization condition.

Findings

The renormalized ratio is shifted by 1/4π times an integer.

The integer quantization condition on the bare parameters is preserved.

Quantum corrections do not break the topological quantization in the broken phase.

Abstract

We consider a spontaneously broken nonabelian topologically massive gauge theory in a broken phase possessing a residual nonabelian symmetry. Recently there has been some question concerning the renormalization of the Chern-Simons coefficient in such a broken phase. We show that, in this broken vacuum, the renormalized ratio of the Chern-Simons coupling to the gauge coupling is shifted by $1/4\pi$ times an integer, preserving the usual integer quantization condition on the bare parameters.