Transport in holographic superfluids

TL;DR

This work develops a controlled holographic description of a relativistic superfluid by constructing a slowly varying, spacetime-dependent solution in AdS/CFT with a large charge $q$. Using gradient expansions and analytic near-transition solutions, the authors compute the transport coefficients of the dual two-fluid system, showing $\eta_s=0$ and $\kappa$ continuous across the phase transition while $\zeta_3$ diverges at the critical temperature; the familiar holographic result $\eta/s=1/(4\pi)$ is recovered and analytic expressions for the backreacted metric near the transition are obtained for a specific model. The results illuminate how the gravity dual encodes superfluid hydrodynamics, including the role of the Goldstone mode and the dissipative channels, and they provide concrete, near-critical predictions for the behavior of bulk viscosities and diffusion in strongly coupled gauge theories. The formalism and explicit solutions offer a tractable framework to study two-fluid dynamics in holographic settings with potential relevance to strongly coupled plasmas and condensed-matter analogs.

Abstract

We construct a slowly varying space-time dependent holographic superfluid and compute its transport coefficients. Our solution is presented as a series expansion in inverse powers of the charge of the order parameter. We find that the shear viscosity associated with the motion of the condensate vanishes. The diffusion coefficient of the superfluid is continuous across the phase transition while its third bulk viscosity is found to diverge at the critical temperature. As was previously shown, the ratio of the shear viscosity of the normal component to the entropy density is 1/(4 pi). As a consequence of our analysis we obtain an analytic expression for the backreacted metric near the phase transition for a particular type of holographic superfluid.