The overlap is not a waveguide

TL;DR

This paper critiques Golterman and Shamir's claim that a modified waveguide model becomes equivalent to the overlap in the limit of many matter fields, clarifying the error in their derivation.

Contribution

The paper identifies and corrects the error in Golterman and Shamir's derivation, clarifying the distinction between the waveguide model and the overlap.

Findings

Golterman and Shamir's claim is incorrect.

The modified waveguide model does not reproduce the overlap.

The overlap model works correctly in the four flavor massless Schwinger model.

Abstract

Golterman and Shamir falsely claim that a waveguide model modified by adding many charged bosonic spinors, in the limit of an infinite number of matter fields, becomes identical to the overlap if in the target theory every fermion appears in four copies. Their modified model would give wrong results even in the vectorial four flavor massless Schwinger model, while a dynamical simulation of this model with the overlap works correctly. In this note we pinpoint the error in the derivation of Golterman and Shamir.