Article

# Superuid black branes in AdS4×S7

Journal of High Energy Physics (Impact Factor: 6.11). 06/2011; 2011(6):1-33. DOI: 10.1007/JHEP06(2011)053

**ABSTRACT**

We consider the d = 3 N = 8 SCFT dual to AdS4 × S7 when held at finite temperature and chemical potential with respect to a diagonal U(1)

R

⊂ SO(8) global symmetry and construct black brane solutions of D = 11 supergravity that are associated with the superfluid instability with the highest known critical temperature. We construct

a rich array of solutions using different sub-truncations of SO(8) gauged supergravity finding results that strongly depend

on the truncation used. Our constructions include black brane solutions associated with the Gubser-Mitra instability which

preserve the U(1)

R

symmetry, and these, in turn, can have further superfluid instabilities. In addition, we also construct superfluid black

branes that at zero temperature are domain walls that interpolate between the SO(8) AdS4 vacuum in the UV, in an alternative quantisation, and the supersymmetric SU(3) × U(1) AdS4 vacuum in the IR.

KeywordsBlack Holes in String Theory–AdS-CFT Correspondence–Holography and condensed matter physics (AdS/CMT)

R

⊂ SO(8) global symmetry and construct black brane solutions of D = 11 supergravity that are associated with the superfluid instability with the highest known critical temperature. We construct

a rich array of solutions using different sub-truncations of SO(8) gauged supergravity finding results that strongly depend

on the truncation used. Our constructions include black brane solutions associated with the Gubser-Mitra instability which

preserve the U(1)

R

symmetry, and these, in turn, can have further superfluid instabilities. In addition, we also construct superfluid black

branes that at zero temperature are domain walls that interpolate between the SO(8) AdS4 vacuum in the UV, in an alternative quantisation, and the supersymmetric SU(3) × U(1) AdS4 vacuum in the IR.

KeywordsBlack Holes in String Theory–AdS-CFT Correspondence–Holography and condensed matter physics (AdS/CMT)

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**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. - [Show abstract] [Hide abstract]

**ABSTRACT:**We continue our study of the retarded Green's function of the universal fermionic supersymmetry current ("supercurrent") for the most general class of d=3 N=2 SCFTs with D=10 or D=11 supergravity duals by studying the propagation of the Dirac gravitino in the electrically charged AdS-Reissner-Nordstr\"om black-brane background of N=2 minimal gauged supergravity in D=4. We expand upon results presented in a companion paper, including the absence of a Fermi surface and the appearance of a soft power-law gap at zero temperature. We also present the analytic solution of the gravitino equation in the AdS_2 X R^2 background which arises as the near-horizon limit at zero temperature. In addition we determine the quasinormal mode spectrum. - [Show abstract] [Hide abstract]

**ABSTRACT:**We investigate spatially modulated instabilities of magnetically charged $AdS_{2}\times\mathbb{R}^2$, $AdS_{3}\times\mathbb{R}^2$ and $AdS_{2}\times\mathbb{R}^3$ backgrounds in a broad class of theories, including those arising from KK reductions of ten and eleven dimensional supergravity. We show that magnetically charged black brane solutions in D=4,5 spacetime dimensions, whose zero temperature near horizon limit approach these backgrounds, can have instabilities that are dual to phases with current density waves that spontaneously break translation symmetry. Our examples include spatially modulated instabilities for a new class of magnetic black brane solutions of D=5 SO(6) gauged supergravity, that we construct in closed form, which are dual to new phases of N=4 SYM theory.

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