Domain Wall Fermions and the Eta Invariant

TL;DR

This paper demonstrates how the phase of the chiral fermion determinant in four dimensions can be reproduced by zero modes bound to a domain wall in five dimensions, with implications for lattice chiral gauge theories.

Contribution

It extends previous work to show the connection between domain wall zero modes and the fermion determinant phase, informing lattice chiral gauge theory formulations.

Findings

Zero modes on domain walls reproduce the fermion determinant phase.

Analysis supports the vacuum overlap approach for chiral gauge theories.

Provides a theoretical foundation for lattice implementations of chiral fermions.

Abstract

We extend work by Callan and Harvey and show how the phase of the chiral fermion determinant in four dimensions is reproduced by zeromodes bound to a domain wall in five dimensions. The analysis could shed light on the applicability of zeromode fermions and the vacuum overlap formulation of Narayanan and Neuberger for chiral gauge theories on the lattice.