A theory of first order dissipative superfluid dynamics

TL;DR

This work derives the most general first-order dissipative relativistic superfluid hydrodynamics in 3+1 dimensions, including parity violation and triangle anomalies, by enforcing Lorentz invariance, time-reversal symmetry, Onsager relations, and the second law through an entropy current with nonnegative divergence. The constitutive relations depend on 20 parameters, partitioned into parity-even (14 dissipative + 0 non-dissipative) and parity-odd (6 non-dissipative, with 2 additional undetermined functions $\sigma_8$ and $\sigma_{10}$) structures; in the collinear limit $\zeta \to 0$ the theory reduces to 7 parameters and a universal relation ties parity-odd coefficients. A holographic AdS/CFT computation with a bulk Chern-Simons term confirms the field-theory predictions in the parity-violating sector, including a nontrivial check of the relation $\tfrac{1}{2}\sigma_{\omega} - \mu \sigma_B = - \dfrac{\mu^3}{3T} c$ in the collinear limit, and demonstrates continuity of parity-odd transport across the phase transition. The results provide a comprehensive framework for parity-violating superfluids, with potential relevance to non-centrosymmetric superconductors and related experiments, and establish a strong link between hydrodynamics and holography via the entropy-current construction.

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.