Is the axial anomaly really determined in a continuous non-perturbative regularization?

TL;DR

This paper investigates how the axial anomaly's value depends on the choice of cutoff functions within a gauge invariant, non-perturbative regularization scheme, revealing that the anomaly's strength is shape-dependent unless additional locality conditions are imposed.

Contribution

It demonstrates that in a gauge invariant non-perturbative regularization, the axial anomaly depends on the cutoff function shape unless the current is local.

Findings

The axial anomaly is cutoff independent but shape-dependent.

Standard anomaly value is recovered under locality assumptions.

Regularization scheme influences anomaly calculation.

Abstract

In the framework of a gauge invariant continuous and non-perturbative regularization scheme based on the smearing of point like interactions by means of cutoff functions, we show that the axial anomaly, though cutoff independent, depends on the shape of the cutoff functions. The standard value for the strength of the axial anomaly is recovered if we assume that the regularized gauge invariant axial current is in addition local.