Holographic superfluidity in imbalanced mixtures

We construct superfluid black hole solutions with two chemical potentials. By analogy with QCD, the two chemical potentials correspond to the baryon and isospin symmetries, respectively. We consider two systems: the back-reacted U( 2) Einstein-Yang-Mills theory in 4+1 dimensions and the 9+1- dimensional D3/D7 brane setup with two coincident D7-brane probes. In the D7-brane model, the identification of baryon and isospin chemical potential is explicit since the dual field theory is explicitly known. Studying the phase diagram, we find in both systems a quantum phase transition at a critical ratio of the two chemical potentials. However the quantum phase transition is different in the two systems: in the D3/D7 brane setup we always find a second order phase transition, while in the Einstein-Yang-Mills theory, depending on the strength of the back-reaction, we obtain a continuous or first order transition. We expect the continuous quantum phase transition to be BKT-like. We comment on the origin of this differing behavior in these apparently very similar models and compare to phenomenological systems.