Simple Evaluation of the Chiral Jacobian with the Overlap Dirac Operator

TL;DR

This paper presents a straightforward method to evaluate the chiral Jacobian using the overlap Dirac operator, accurately determining the chiral anomaly coefficient without gauge coupling expansion.

Contribution

It introduces a simple calculational scheme for the chiral Jacobian that works in the continuum limit for general parameters, enhancing understanding of lattice chiral symmetry.

Findings

Explicit evaluation of the chiral Jacobian in the continuum limit.

Determination of the chiral anomaly coefficient for various parameters.

Validation of the calculational scheme's simplicity and effectiveness.

Abstract

The chiral Jacobian, which is defined with Neuberger's overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and straightforward. We determine a coefficient of the chiral anomaly for general values of the mass parameter and the Wilson parameter of the overlap Dirac operator.