Axial anomaly with the overlap-Dirac operator in arbitrary dimensions

TL;DR

This paper computes the classical continuum limit of the lattice axial anomaly using the overlap-Dirac operator across arbitrary even dimensions, confirming its relation to the Chern character.

Contribution

It provides a systematic calculation method for the axial anomaly's continuum limit in arbitrary even dimensions using the overlap-Dirac operator.

Findings

The continuum limit matches the Chern character form.

The method applies to arbitrary even dimensions.

The approach confirms the topological nature of the anomaly.

Abstract

We evaluate for arbitrary even dimensions the classical continuum limit of the lattice axial anomaly defined by the overlap-Dirac operator. Our calculational scheme is simple and systematic. In particular, a powerful topological argument is utilized to determine the value of a lattice integral involved in the calculation. When the Dirac operator is free of species doubling, the classical continuum limit of the axial anomaly in various dimensions is combined into a form of the Chern character, as expected.