Large Gauge Invariance in NonAbelian Finite Temperature Effective Actions

TL;DR

This paper investigates large gauge invariance in nonabelian finite temperature quantum field theories, revealing topological structures and their implications for effective actions, especially in relation to Chern-Simons terms and Wilson loops.

Contribution

It provides an invariant characterization of fluxes in finite temperature effective actions and relates them to topological indices measuring obstructions to diagonalization.

Findings

Relation of fluxes to a topological index

Explicit realizations of large gauge transformations with non-zero index

Analysis of large gauge invariance in various topologies

Abstract

We analyze large gauge invariance in combined nonabelian and thermal QFT and their physical consequences for D=3 effective actions. After briefly reviewing the structure of bundles and large gauge transformations that arise in non-simply connected 3-manifolds and gauge groups, we discuss their connections to Chern-Simons terms and Wilson-Polyakov loops. We then provide an invariant characterization of the ``abelian'' fluxes encountered in explicit computations of finite temperature effective actions. In particular we relate, and provide explicit realizations of, these fluxes to a topological index that measures the obstruction to global diagonalization of the loops around compactified time. We also explore the fate of, and exhibit some everywhere smooth, large transformations for non-vanishing index in various topologies.