Gauge Invariance, Finite Temperature and Parity Anomaly in D=3

TL;DR

This paper demonstrates how gauge invariance at finite temperature in 3D gauge theories can be maintained through regularization, revealing the role of parity anomalies and the non-perturbative nature of large gauge transformations.

Contribution

It shows that gauge invariance at finite temperature can be achieved via regularization, clarifying the non-perturbative effects of large gauge transformations and parity anomalies in 3D gauge theories.

Findings

Gauge invariance can be preserved at finite temperature with suitable regularization.

Large gauge transformations are non-perturbative and affect Ward identities.

The temperature dependence of the Chern-Simons term is explained through non-perturbative effects.

Abstract

The effective gauge field actions generated by charged fermions in $QED_3$ and $QCD_3$ can be made invariant under both small and large gauge transformations at any temperature by suitable regularization of the Dirac operator determinant, at the price of parity anomalies. We resolve the paradox that the perturbative expansion is not invariant, as manifested by the temperature dependence of the induced Chern-Simons term, by showing that large (unlike small) transformations and hence their Ward identities, are not perturbative order-preserving. Our results are illustrated through concrete examples of field configurations.