Superconductivity from D3/D7: holographic pion superfluid

We show that a D3/D7 system (in the limit of zero quark mass) at finite isospin chemical potential goes through a superconductor (superfluid) like phase transition. This is similar to a flavored superfluid phase studied in the QCD literature, where mesonic operators condense. We have studied the frequency dependent conductivity of the condensate and found a delta function peak in the zero frequency limit. This is an example of superconductivity in a string theory context. Consequently we have found a superfluid/supercurrent type solution and studied the associated phase diagram. The superconducting transition changes from second order to first order at a critical superfluid velocity. We have studied various properties of the superconducting system like superfluid density, energy gap, second sound etc. We investigate the possibility of the isospin chemical potential modifying the embedding of the flavor branes by checking whether the transverse scalars also condense at low temperatures. This however does not seem to be the case.