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 Sigma(3) x S-4, where Sigma(3) = H-3/Gamma, S-3/Gamma or R-3/Gamma where Gamma 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) x G(2(2))/SO(4). When Sigma(3) = H-3/Gamma the D = 4 theory has an AdS(4) vacuum which uplifts to the known supersymmetric AdS(4) x H-3/Gamma x S-4 solution of D = 11 supergravity that describes the N = 2 d = 3 SCFT arising when M5-branes wrap SLag 3-cycles H-3/Gamma in Calabi-Yau three-folds. We use the KK reduction for Sigma(3) = H-3/Gamma 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 similar to 39.