Wrapped M5-branes, consistent truncations and AdS/CMT

Abstract

At the level of the bosonic fields, we construct consistent Kaluza--Klein reductions of D=11 supergravity on ${\Sigma }_3\times S^4$, 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 $SU(1,1)/U(1)\times G_{2(2)}/SO(4)$. %, and the gauging is only in the hypermultiplet When ${\Sigma }_3=H^3/\Gamma$ the D=4 theory has an $Ad{S}_4$ vacuum which uplifts to the known supersymmetric $Ad{S}_4\times H^3/\Gamma \times S^4$ 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 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 $z\sim 39$.

47 pages, reference added, typos corrected. Published version

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