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 ${\mathrm{\Sigma }}_3\times S^4$, where ${\mathrm{\Sigma }}_3=H^3\mathrm{/}\mathrm{\Gamma },S^3\mathrm{/}\mathrm{\Gamma }$ or $R^3\mathrm{/}\mathrm{\Gamma }$ where $\mathrm{\Gamma }$ 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 $SU(1,1)\mathrm{/}U(1)\times G_{2(2)}\mathrm{/}SO(4)$. %, and the gauging is only in the hypermultiplet When ${\mathrm{\Sigma }}_3=H^3\mathrm{/}\mathrm{\Gamma }$ the D=4 theory has an $Ad{S}_4$ vacuum which uplifts to the known supersymmetric $AdS_4\times H^3/\Gamma\times S^4$solutionofD=11supergravitythatdescribestheN=2$d=3$ SCFT arising when M5-branes wrap SLag 3-cycles $H^3\mathrm{/}\mathrm{\Gamma }$ in Calabi-Yau three-folds. We use the KK reduction for ${\mathrm{\Sigma }}_3=H^3\mathrm{/}\mathrm{\Gamma }$ 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 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 $z\sim 39$.