Temperature dependence of the anomalous effective action of fermions in two and four dimensions

TL;DR

This paper calculates how the anomalous effective action of fermions depends on temperature in two and four dimensions, confirming compatibility with axial anomaly saturation and existing theoretical results.

Contribution

It provides the leading-order temperature dependence of the anomalous effective action, preserving chiral symmetry and extending previous theoretical understandings.

Findings

Temperature dependence is compatible with axial anomaly saturation.

Results confirm soft-pions theorems at zero temperature.

Matches recent literature on pionic decay amplitudes.

Abstract

The temperature dependence of the anomalous sector of the effective action of fermions coupled to external gauge and pseudo-scalar fields is computed at leading order in an expansion in the number of Lorentz indices in two and four dimensions. The calculation preserves chiral symmetry and confirms that a temperature dependence is compatible with axial anomaly saturation. The result checks soft-pions theorems at zero temperature as well as recent results in the literature for the pionic decay amplitude into static photons in the chirally symmetric phase. The case of chiral fermions is also considered.