Holographic Superconductors from Gauged Supergravity

TL;DR

This work advances a top-down holographic program for superconductivity by truncating ${\cal N}=8$ SO(6)$ gauged supergravity to a $U(1)^3$ sector and systematically studying charged hairy black holes at fixed charge densities. It introduces two non-supersymmetric truncations (I and II) alongside a supersymmetric one, derives their equations of motion and AdS asymptotics, and analyzes hair formation across one-, two-, and three-charge configurations within the STU framework. The key findings include second-order phase transitions with hair in several sectors, plus retrograde condensation where hairy solutions are thermodynamically subdominant at high temperatures; in the three-charge ensemble, sector II provides the dominant condensation channel, corresponding to operators of dimension 3 in the dual ${\cal N}=4$ SYM. Collectively, the results illuminate the phase structure of large-$N$ SYM with fixed charge densities and lay groundwork for a more complete top-down phase diagram in holographic superconductivity.

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.