Regulated chiral gauge theory and the strong CP problem

TL;DR

This paper proposes a five-dimensional lattice formulation of chiral gauge theories, including the Standard Model, which potentially resolves the strong CP problem by leveraging fermion zero modes localized in the extra dimension.

Contribution

It introduces a novel five-dimensional lattice approach to chiral gauge theories that naturally avoids the strong CP problem and the U(1)_A problem, differing from traditional four-dimensional formulations.

Findings

QCD embedded in this framework appears free from the strong CP problem.

Fermion zero modes localized in the fifth dimension play a central role.

The approach differs from conventional lattice QCD formulations.

Abstract

Four-dimensional chiral gauge theory can be formulated as the boundary theory on a five-dimensional manifold in a manner that may be realized on a finite lattice. There are interesting features of these theories which defy a purely four-dimensional conception of universality. We find that QCD when embedded in a chiral gauge theory (the Standard Model) and regulated this way appears to suffer neither from a $U(1)_A$ problem nor a strong $CP$ problem, with a central role played by fermion zeromodes localized far away in the fifth dimension. In this way it differs from conventional lattice QCD formulated as a stand-alone theory. Our analysis builds on recent work by others that highlights the role of global $U(1)$ symmetries in five dimensional formulations of four-dimensional chiral gauge theories, and the generic appearance of fermion zeromodes in the bulk.