Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson lattice Dirac operator

TL;DR

This paper demonstrates through perturbation theory that a Ginsparg-Wilson lattice Dirac operator can correctly reproduce the axial anomaly and topological charge density in the continuum limit, even without zero modes in certain gauge backgrounds.

Contribution

It provides a perturbative calculation confirming the axial anomaly reproduction of a proposed Ginsparg-Wilson operator without zero modes.

Findings

Recovers topological charge density in continuum limit

Validates the proposed operator's anomaly reproduction

Supports the operator's exponential locality and doublers-free properties

Abstract

A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac operator does not possess any topological zero modes in topologically-nontrivial gauge backgrounds, it can reproduce correct axial anomaly for sufficiently smooth gauge configurations, provided that it is exponentially-local, doublers-free, and has correct continuum behavior. In this paper, we calculate the axial anomaly of this lattice Dirac operator in weak coupling perturbation theory, and show that it recovers the topological charge density in the continuum limit.