Superfluid black branes in AdS4 × S7

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.