The relation between the waveguide and overlap implementations of Kaplan's domain wall fermions

TL;DR

This paper compares the overlap and waveguide implementations of Kaplan's domain wall fermions, revealing that the overlap effective action matches a modified waveguide model with ghost fields, raising concerns about its viability for lattice chiral gauge theories.

Contribution

It demonstrates the equivalence between the overlap formula and a modified waveguide model with ghost fields, questioning the overlap approach's suitability for chiral gauge theories.

Findings

Overlap effective action equals a waveguide model with ghosts.

Raises questions about the overlap formula's viability.

Implications for lattice chiral gauge theory formulations.

Abstract

Recently, Narayanan and Neuberger proposed that the fermion determinant for a lattice chiral gauge theory be defined by an overlap formula. The motivation for that formula comes from Kaplan's five dimensional lattice domain wall fermions. In the case that the target continuum theory contains $4n$ chiral families, we show that the effective action defined by overlap formula is identical to the effective action of a modified waveguide model that has extra bosonic ghost fields. This raises serious questions about the viability of the overlap formula for defining chiral gauge theories on the lattice.