Finite Temperature Perturbation Theory and Large Gauge Invariance

TL;DR

This paper investigates finite temperature perturbation theory in Chern-Simons models, demonstrating how large gauge invariance is maintained at all orders despite perturbative violations, with insights potentially extending to higher dimensions.

Contribution

It shows how large gauge invariance is preserved at all orders in finite temperature perturbation theory for Chern-Simons theories, using a simplified 0+1-dimensional model.

Findings

Nonextensive terms appear in the finite temperature effective action.

Large gauge invariance is restored at all orders in perturbation theory.

Insights may extend to higher-dimensional Chern-Simons theories.

Abstract

We examine finite temperature perturbation theory for Chern-Simons theories, in the context of an analogue 0+1-dimensional model. In particular, we show how nonextensive terms arise in the perturbative finite temperature effective action, using both the real-time and imaginary-time formalisms. We illustrate how large gauge invariance is restored at all orders, despite being broken at any given order in perturbation theory. We discuss which aspects generalize to a perturbative analysis of finite temperature Chern-Simons terms in higher dimensions.