Galilean Anomalies and Their Effect on Hydrodynamics

TL;DR

This paper explores how gauge and gravitational anomalies manifest in Galilean theories with torsion, extending relativistic anomaly inflow mechanisms and analyzing their impact on hydrodynamics and entropy currents.

Contribution

It extends null background construction to include torsion and spin currents, establishing how anomalies influence Galilean hydrodynamics and entropy in a novel formalism.

Findings

Galilean anomalies only in even dimensions

Anomalies affect gauge and rotational symmetries, not Milne boosts

Different entropy currents in two formalisms, with gravitational anomaly contribution

Abstract

We extend the null background construction of [arXiv:1505.05677,arXiv:1509.04718] to include torsion and a conserved spin current, and use it to study gauge and gravitational anomalies in Galilean theories coupled to torsional Newton-Cartan backgrounds. We establish that the relativistic anomaly inflow mechanism with an appropriately modified anomaly polynomial, can be used to generate these anomalies. Similar to relativistic case, we find that Galilean anomalies also survive only in even dimensions. Further, these anomalies only effect the gauge and rotational symmetries of a Galilean theory; in particular the Milne boost symmetry remains non-anomalous. We also extend the transgression machinery used in relativistic fluids to fluids on null backgrounds, and use it to determine how these anomalies affect the constitutive relations of a Galilean fluid. Unrelated to Galilean fluids, we propose an analogue of the off-shell second law of thermodynamics for relativistic fluids introduced by [arXiv:1106.0277], to include torsion and a conserved spin current in Vielbein formalism. Interestingly, we find that even in absense of spin and torsion the entropy currents in two formalisms are different; while the usual entropy current gets a contribution from gravitational anomaly, the entropy current in Vielbein formalism does not have any anomaly induced part.