Non-Abelian Anomalous (Super)Fluids in Thermal Equilibrium from Differential Geometry

TL;DR

This paper uses differential geometry to derive the equilibrium partition function for non-Abelian anomalous superfluids, revealing how anomalies influence hydrodynamic properties and gauge currents.

Contribution

It provides a general method to compute the anomaly-induced partition function for superfluids using differential geometry and applies it to non-Abelian cases.

Findings

Explicit formulas for invariant and anomalous partition functions

Derived gauge currents and energy-momentum tensors in anomalous superfluids

Applied the method to Wess-Zumino-Witten action for Goldstone modes

Abstract

We apply differential geometry methods to the computation of the anomaly-induced hydrodynamic equilibrium partition function. Implementing the imaginary-time prescription on the Chern-Simons effective action on a stationary background, we obtain general closed expressions for both the invariant and anomalous part of the partition function. This is applied to the Wess-Zumino-Witten action for Goldstone modes, giving the equilibrium partition function of superfluids. In all cases, we also study the anomaly-induced gauge currents and energy-momentum tensor, providing explicit expressions for them.