More on axial anomalies of Lifshitz fermions

TL;DR

This paper demonstrates that the axial anomaly for Lifshitz fermions with arbitrary anisotropy scaling is identical to the relativistic case, and introduces models for baryon and lepton number violation in non-relativistic gravity theories.

Contribution

It extends the understanding of axial anomalies in Lifshitz fermions to arbitrary scaling exponents and presents new models for symmetry violation in non-relativistic gravity.

Findings

Axial anomaly matches the relativistic case for all z.

New models realize baryon and lepton number violation.

Space volume has a lower bound set by gravitational parameters.

Abstract

We show that the gauge and metric field contribution to the axial anomaly of a four-dimensional massless Lifshitz fermion theory with anisotropy scaling exponent z is identical to the relativistic case, hereby extending the results found in arXiv:1103.5693 to arbitrary values of z. This is in accordance with the fact that the axial anomaly is an infra-red phenomenon in disguise. We also provide some new models that realize baryon and lepton number violation in non-relativistic theories of gravity. In all cases, the volume of space exhibits a lower bound that is fixed by the gravitational coupling parameters.