Holographic model of superfluidity

We study a holographic model of a relativistic quantum system with a global $U(1)$ symmetry, at nonzero temperature and density. When the temperature falls below a critical value, we find a second-order superfluid phase transition with mean-field critical exponents. In the symmetry-broken phase, we determine the speed of second sound as a function of temperature. As the velocity of the superfluid component relative to the normal component increases, the superfluid transition goes through a tricritical point and becomes first order.