Gravity derivation of the Tisza-Landau model in AdS/CFT

We derive the fully backreacted bulk solution dual to a boundary superfluid with finite supercurrent density in AdS/CFT. The nonlinear boundary hydrodynamical description of this solution is shown to be governed by a relativistic version of the Tisza-Landau two-fluid model to nondissipative order. As previously noted, the phase transition can be both first order and second order, but in the strongly backreacted regime at low charge q we find that the transition remains second order for all allowed fractions of superfluid density.