3 Into 2 Doesn't Go: (almost) chiral gauge theory on the lattice

TL;DR

This paper investigates a novel lattice chiral gauge theory that, while successfully reproducing some features of the continuum theory, fails to capture fermion nonconservation in the 2D axial Schwinger model.

Contribution

It explores the applicability of Kaplan's higher-dimensional lattice approach to 2D chiral gauge theories, highlighting both successes and limitations.

Findings

Perturbation expansion matches continuum results

Fails to reproduce fermion nonconservation in 2D

Highlights challenges in lattice chiral gauge theories

Abstract

Kaplan recently proposed a novel lattice chiral gauge theory in which the bare theory is defined on $(2n+1)$-dimensions, but the continuum theory emerges in $2n$-dimensions. We explore whether the resulting theory reproduces all the features of continuum chiral gauge theory in the case of two-dimensional axial Schwinger model. We find that one can arrange for the two-dimensional perturbation expansion to be reproduced successfully. However, the theory fails to reproduce the 2-dimensional fermion nonconservation.