Kaplan-Narayanan-Neuberger lattice fermions pass a perturbative test

TL;DR

This paper evaluates the Kaplan-Narayanan-Neuberger lattice fermion scheme using the chiral Schwinger model, confirming it reproduces key continuum features like gauge invariance and anomalies, indicating its potential as a valid chiral gauge theory regularization.

Contribution

It provides a perturbative validation of the KNN scheme's effectiveness in reproducing continuum chiral gauge theory features on the lattice.

Findings

Reproduces the effective action with gauge invariance in the real part.

Correctly reproduces the continuum anomaly in the imaginary part.

Indicates the scheme's potential as a proper lattice regularization.

Abstract

We test perturbatively a recent scheme for implementing chiral fermions on the lattice, proposed by Kaplan and modified by Narayanan and Neuberger, using as our testing ground the chiral Schwinger model. The scheme is found to reproduce the desired form of the effective action, whose real part is gauge invariant and whose imaginary part gives the correct anomaly in the continuum limit, once technical problems relating to the necessary infinite extent of the extra dimension are properly addressed. The indications from this study are that the Kaplan--Narayanan--Neuberger (KNN) scheme has a good chance at being a correct lattice regularization of chiral gauge theories.