On Holographic p-wave Superfluids with Back-reaction

TL;DR

This paper numerically constructs holographic p-wave superfluid models with back-reaction, revealing a transition from second to first order at a critical back-reaction strength, enriching the understanding of phase transitions in gauge-gravity duality.

Contribution

It provides the first fully back-reacted holographic p-wave superfluid solutions, showing how the order of the phase transition depends on the back-reaction parameter.

Findings

Transition changes from second to first order at alpha_c=0.365

Back-reaction significantly affects the phase transition nature

Constructs fully back-reacted solutions beyond probe limit

Abstract

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 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's 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's equation, and find that for values of alpha above a critical value alpha_c = 0.365 +- 0.001, the transition becomes first order.