Lorentz symmetry violation in the fermion number anomaly with the chiral overlap operator

TL;DR

This paper investigates the fermion number anomaly in a lattice formulation of chiral gauge theories, revealing a Lorentz-violating term that cancels when gauge anomaly conditions are satisfied.

Contribution

It computes the classical continuum limit of the fermion number anomaly in a new lattice formulation, uncovering Lorentz symmetry violation linked to gauge anomaly cancellation.

Findings

Lorentz-violating term appears in the continuum limit

The Lorentz violation is proportional to the gauge anomaly coefficient

Lorentz invariance is restored when the gauge anomaly cancels

Abstract

Recently, Grabowska and Kaplan proposed a four-dimensional lattice formulation of chiral gauge theories on the basis of a chiral overlap operator. We compute the classical continuum limit of the fermion number anomaly in this formulation. Unexpectedly, we find that the continuum limit contains a term which is not Lorentz invariant. The term is, however, proportional to the gauge anomaly coefficient, and thus the fermion number anomaly in this lattice formulation automatically restores the Lorentz-invariant form when and only when the anomaly cancellation condition is met.