The many phases of holographic superfluids
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We investigate holographic superfluids in AdSd+1 with d =3, 4 in the nonbackreacted approximation for various masses of the scalar field. In d =3 the phase structure is universal for all the masses that we consider: the critical temperature decreases as the superfluid velocity increases, and as it is cranked high enough, the order of the phase transition changes from second to first. Surprisingly, in d = 4 we find that the phase structure is more intricate. For sufficiently high mass, there is always a second order phase transition to the normal phase, no matter how high the superfluid velocity. For some parameters, as we lower the temperature, this transition happens before a first order transition to a new super conducting phase. Across this first order transition, the gap in the transverse conductivity jumps from almost zero to about half its maximum value. We also introduce a double scaling limit where we can study the phase transitions(semi-)analytically in the large velocity limit. The results corroborate and complement our numerical results. In d =4, this approach has the virtue of being fully analytically tractable.