Chiral gauge theory at the boundary between topological phases

TL;DR

This paper presents a new approach to realize chiral fermions with gauge symmetry on the boundary of higher-dimensional topological phases, avoiding mirror partners and enabling lattice regularization of chiral gauge theories.

Contribution

It introduces a boundary-based method for constructing chiral gauge theories that ensures anomaly cancellation and locality, advancing lattice regularization techniques.

Findings

Chiral fermions can appear on boundary without mirror partners.

Gauge anomalies must cancel for locality.

Potential for lattice implementation of chiral gauge theories.

Abstract

I demonstrate how chiral fermions with an exact gauge symmetry can appear on the d-dimensional boundary of a finite volume (d+1)-dimensional manifold, without any light mirror partners. The condition for the d-dimensional boundary theory to be local is that gauge anomalies cancel and that the volume be large. This can likely be achieved on a lattice and provides a new paradigm for the lattice regularization of chiral gauge theories.