Conserved currents in five-dimensional proposals for lattice chiral gauge theories

TL;DR

This paper investigates the application of the Grabowska-Kaplan framework to lattice QCD, revealing the emergence of a conserved axial current that could lead to unphysical particles, and discusses implications for lattice chiral gauge theories.

Contribution

It demonstrates the presence of a conserved, gauge-invariant axial current in lattice QCD using the Grabowska-Kaplan approach, highlighting potential issues for chiral gauge theory constructions.

Findings

Presence of a conserved singlet axial current in the framework

Potential emergence of a superfluous Nambu-Goldstone boson

Identification of similar issues in the disk formalism

Abstract

We apply the Grabowska-Kaplan framework, originally proposed for lattice chiral gauge theories, to QCD. We show that the resulting theory contains a conserved and gauge invariant singlet axial current, both on the lattice and in the continuum limit. This must give rise to a difference with QCD, with the simplest possibility being a superfluous Nambu-Goldstone boson in the physical spectrum not present in QCD. We find a similar unwanted conserved current in the recent "disk" formalism [Kaplan, Kaplan & Sen], this time limiting ourselves to the continuum formulation. A similar problem is expected when either of these formalisms is used for its original goal of constructing lattice chiral gauge theories. Finally we discuss a conjecture about the possible dynamics that might be associated with the unwanted conserved current, and the fate of 't Hooft vertices.