Torsion and anomalies in the warped limit of Lifschitz theories

TL;DR

This paper investigates the anomalous behavior of fermionic Lifschitz theories in the limit of small anisotropic scaling, revealing a mixed boost-translation anomaly linked to torsion in a Newton-Cartan geometric framework.

Contribution

It demonstrates the emergence of a mixed boost-translation anomaly in Lifschitz theories with small anisotropic scaling and connects this to torsion in Newton-Cartan geometry, providing an effective field theory perspective.

Findings

Identification of a mixed boost-translation anomaly

Connection between torsion and anomalies in Newton-Cartan geometry

Effective field theory description of anomalous transport coefficients

Abstract

We describe the physics of fermionic Lifschitz theories once the anisotropicscaling exponent is made arbitrarily small. In this limit the system acquires an enhanced(Carrollian) boost symmetry. We show, both through the explicit computation of the pathintegral Jacobian and through the solution of the Wess-Zumino consistency conditions, thatthe translation symmetry in the anisotropic direction becomes anomalous. This turns outto be a mixed anomaly between boosts and translations. In a Newton-Cartan formulationof the space-time geometry such anomaly is sourced by torsion. We use these results togive an effective field theory description of the anomalous transport coefficients, which wereoriginally computed through Kubo formulas in [1]. Along the way we provide a link withwarped CFTs.