On holographic p-wave superfluids with back-reaction

We numerically construct asymptotically Anti-de Sitter charged black hole solutions of (4+1)-dimensional SU(2) Einstein-Yang-Mills theory that, for sufficiently low temperature, develop vector hair. Via gauge-gravity duality, these solutions describe a strongly-coupled conformal field theory at finite temperature and density that undergoes a phase transition to a superfluid state with spontaneously broken rotational symmetry (a p-wave superfluid state). The bulk theory has a single free parameter, the ratio of the five-dimensional gravitational constant to the Yang-Mills coupling, which we denote as α. Previous analyses have shown that in the so-called probe limit, where α goes to zero and hence the gauge fields are ignored in Einstein's equation, the transition to the superfluid state is second order. We construct fully back-reacted solutions, where α is finite and the gauge fields are included in Einstein's equation, and find that for values of α above a critical value αc=0.365±0.001 in units of the AdS radius, the transition becomes first order.