Path integral analysis of the axial anomaly in Very Special Relativity

TL;DR

This paper revisits the axial anomaly within Very Special Relativity using Fujikawa's path integral method, demonstrating the absence of VSR contributions in the measure across various dimensions and spacetime geometries.

Contribution

It provides a nonperturbative analysis showing no VSR effects in the axial anomaly measure in multiple spacetime settings.

Findings

No VSR contribution in (3+1) dimensions

Extension of results to (1+1) dimensions

Application to two-dimensional curved spacetime

Abstract

In this note, we revise the problem of the axial anomaly in the framework of very special relativity following Fujikawa's path integral approach. We show nonperturbatively that no VSR contribution is present in the path integral measure in $(3+1)$-dimensional spacetime. Furthermore, we extend our results to $(1+1)$ dimensions, as well as to the two-dimesional curved spacetime.