Why the overlap formula does not lead to chiral fermions

TL;DR

The paper critically examines the overlap approach for lattice chiral gauge theories, demonstrating its limitations through a waveguide model equivalence and raising doubts about its viability.

Contribution

It introduces a simple test for the overlap approach and shows its potential shortcomings, challenging previous assumptions about its effectiveness.

Findings

The overlap formula is equivalent to a waveguide model for trivial gauge configurations.

This equivalence reveals fundamental issues with the overlap approach.

The paper casts serious doubts on the viability of the overlap method for chiral fermions.

Abstract

We describe a conceptually simple, but important test for the overlap approach to the construction of lattice chiral gauge theories. We explain the equivalence of the overlap formula with a certain waveguide model for a simple set of gauge configurations (the trivial orbit). This equivalence is helpful in carrying out the test, and casts serious doubts on the viability of the overlap approach. A recent note by Narayanan and Neuberger which points out a mistake in our previous work is irrelevant in this context.