Chiral Anomaly at Infinite Temperature

TL;DR

This paper demonstrates that the Abelian chiral anomaly becomes ill-defined at infinite temperature due to limit ambiguities, contrasting with its well-defined nature at finite temperatures.

Contribution

It reveals the ambiguity in the chiral anomaly's behavior at infinite temperature caused by the order of limits, a novel insight into anomaly regularization.

Findings

Chiral anomaly is ill-defined at infinite temperature.

Order of limits affects the anomaly calculation.

Different results emerge based on limit ordering.

Abstract

Using the heat kernel regularization we show that the Abelian chiral anomaly in the limit of infinite temperature it is not a well defined quantity, contrary to what happens at any finite temperature. We show that there is an ambiguity in the ordering of the limits of infinite temperature and removal of the cut-off so that changing this ordering we find different results for the chiral anomaly. We discuss these cases and their possible interpretation.