On Holographic p-wave Superfluids with Back-reaction

Abstract

We numerically construct asymptotically Anti-de Sitter charged black hole solutions of (4_s161)-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 alpha. Previous analyses have shown that in the so-called probe limit, where alpha goes to zero and hence the gauge fields are ignored in Einstein_s14s equation, the transition to the superfluid state is second order. We construct fully back-reacted solutions, where alpha is finite and the gauge fields are included in Einstein_s14s equation, and find that for values of alpha above a critical value alpha_c = 0.365 _s16- 0.001, the transition becomes first order.