On the Quantization of the Abelian Chern-Simons Coefficient at Finite Temperature

TL;DR

This paper demonstrates that in Abelian Chern-Simons theory coupled to matter fields, gauge invariance at finite temperature enforces the quantization of the Chern-Simons coefficient and its quantum corrections, akin to non-Abelian theories.

Contribution

It extends the understanding of Chern-Simons coefficient quantization to Abelian theories at finite temperature with non-zero magnetic flux.

Findings

Chern-Simons coefficient is quantized at finite temperature.

Quantum corrections preserve the quantization condition.

Gauge invariance constrains the theory at finite temperature.

Abstract

We show that when the Abelian \CS\ theory coupled to matter fields is quantized in a vacuum with non vanishing magnetic flux (or electric charge), the requirement of gauge invariance at finite temperature leads to the quantization of the \CS\ coefficient and its quantum corrections, in a manner similar to the non-Abelian case.