Anomalies in Superfluids and a Chiral Electric Effect

TL;DR

This work extends relativistic superfluid hydrodynamics to include an arbitrary number of unbroken charges and analyzes chiral transport via entropy constraints. It organizes the resulting first-order chiral terms, linking certain coefficients to anomalies, notably the $JJJ$ triangle anomaly for the chiral electric conductivity $c^{abc}$, and discusses their Onsager structure and CPT restrictions. The authors reinterpret known normal-fluid chiral terms in light of anomaly considerations and propose educated guesses for the superfluid terms, including a generalized chiral electric effect and the vanishing of the would-be $JJT$-type contributions, supported by a hierarchical anomaly-based interpretation. The results offer a framework to connect anomalous transport in superfluids with underlying gauge-mandated and gravitational anomalies, with potential implications for neutron-star matter and CFL-like phases in QCD, and they set the stage for microscopic verification and experimental exploration.

Abstract

We analyze the chiral transport terms in relativistic superfluid hydrodynamics. In addition to the spontaneously broken symmetry current, we consider an arbitrary number of unbroken symmetries and extend the results of arXiv:1105.3733. We suggest an interpretation of some of the new transport coefficients in terms of chiral and gravitational anomalies. In particular, we show that with unbroken gauged charges in the system, one can observe a chiral electric conductivity - a current in a perpendicular direction to the applied electric field. We present a motivated proposal for the value of the associated transport coefficient, linking it to the triangle anomaly. Along the way we present new arguments regarding the interpretation of the anomalous transport coefficients in normal fluids. We propose a natural generalization of the chiral transport terms to the case of an arbitrary number of spontaneously broken symmetry currents.