Transport in holographic superfluids

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.