A theory of first order dissipative superfluid dynamics

TL;DR

This paper derives the most general relativistic superfluid hydrodynamics equations at first order, including parity-violating effects, and verifies these results using holographic models.

Contribution

It provides a comprehensive, Lorentz-invariant formulation of superfluid dynamics with parity violation, extending standard models and confirming results via holography.

Findings

Derived the most general first-order superfluid equations respecting symmetries.

Identified a 20-parameter set of equations, reducing to 7 parameters at small velocities.

Validated the theoretical framework with holographic computations.

Abstract

We determine the most general form of the equations of relativistic superfluid hydrodynamics consistent with Lorentz invariance, time-reversal invariance, the Onsager principle and the second law of thermodynamics at first order in the derivative expansion. Once parity is violated, either because the $U(1)$ symmetry is anomalous or as a consequence of a different parity-breaking mechanism, our results deviate from the standard textbook analysis of superfluids. Our general equations require the specification of twenty parameters (such as the viscosity and conductivity). In the limit of small relative superfluid velocities we find a seven parameter set of equations. In the same limit, we have used the AdS/CFT correspondence to compute the parity odd contributions to the superfluid equations of motion for a generic holographic model and have verified that our results are consistent.