Wrapped M5-branes, consistent truncations and AdS/CMT

At the level of the bosonic fields, we construct consistent Kaluza-Klein reductions of D = 11 supergravity on Σ3 × S4, where Σ3 = H3/Γ, S3/Γ or R3/Γ where Γ is a discrete group of isometries. The result is the bosonic content of an N = 2 D = 4 gauged supergravity with a single vector multiplet and two hypermultiplets, whose scalar fields parametrise SU(1,1)/U(1) × G2(2)/SO(4). When Σ3 = H3/Γ the D = 4 theory has an AdS4 vacuum which uplifts to the known supersymmetric AdS4 × H3/Γ × S4 solution of D = 11 supergravity that describes the N = 2 d = 3 SCFT arising when M5-branes wrap SLag 3-cycles H3/Γ in Calabi-Yau three-folds. We use the KK reduction for Σ3 = H3/Γ to construct D = 11 black hole solutions that describe these d = 3 SCFTs at finite temperature and charge density and show that there is a superconducting instability involving a charged scalar field, and another instability involving neutral fields including both scalar and vector fields. We also use this KK reduction to construct a D = 11 Lifshitz solution that is dual to a d = 3 field theory with dynamical exponent z ∼ 39.