Gauge covariant heat kernel expansion at finite temperature

TL;DR

This paper extends the heat kernel method to finite temperature gauge theories, emphasizing the importance of the Polyakov loop alongside the field strength for gauge covariance, revealing the Aharonov-Bohm effect's role.

Contribution

It introduces a gauge covariant heat kernel expansion at finite temperature by incorporating the Polyakov loop, addressing limitations of previous methods.

Findings

Polyakov loop is essential for gauge covariant heat kernel expansion.

The Aharonov-Bohm effect influences gauge field characterization at finite temperature.

Generalized Seeley-DeWitt coefficients are obtained with gauge covariance.

Abstract

The heat kernel method is extended to the case of finite temperature. Special emphasis is given to the study of gauge theories. Due to the compactness of space in the Euclidean time direction (inverse temperature) the field strength cannot completely characterize the gauge fields. This is just a manifestation of the Aharonov-Bohm effect. The field strength has to be supplemented by the Polyakov loop. Only if the latter is taken into account one obtains gauge covariant results for the generalized Seeley-DeWitt coefficients of the heat kernel expansion.