Kaplan-Narayanan-Neuberger lattice fermions pass a perturbative test

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.