Holographic Superconductors from Gauged Supergravity

TL;DR

This paper investigates phase transitions and instabilities in holographic superconductors derived from gauged supergravity, revealing new insights into the phase diagram of large N super Yang-Mills theory with fixed charge densities.

Contribution

It introduces a detailed analysis of phase transitions involving U(1) symmetry breaking in truncated gauged supergravity models, including back-reaction effects and thermodynamical stability.

Findings

Identification of second order phase transitions with hairy black holes.

Discovery of unstable branches extending above critical temperatures.

Insights into the phase structure of large N super Yang-Mills theory.

Abstract

We consider minimal setups arising from different truncations of N=8 five-dimensional SO(6) gauged supergravity to study phase transitions involving spontaneous breaking of any of the U(1) symmetries in U(1)xU(1)xU(1)in SO(6). These truncations only keep the three relevant vector fields, four complex scalar fields carrying U(1) charges, plus two neutral scalar fields required by consistency. By considering thermal ensembles with different fixed U(1) charge densities and solving the complete equations including the full back-reaction, in some cases we find instabilities towards the formation of hairy black holes, which lead to second order transitions, resulting from a thermodynamical competition between different sectors. We argue that these should be the dominant thermodynamical instabilities in the full ten-dimensional type IIB theory. In other cases we find unstable branches of hairy black holes that extend to temperatures above a critical temperature (`retrograde condensation'). The results can be used as a first step to understand new aspects of the phase diagram of large N, N=4 SU(N) super Yang-Mills theory with fixed charge densities.