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High Energy Physics - Theory, hep-th
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 $SU(1,1)/U(1)\times G_{2(2)}/SO(4)$. When
$\Sigma_3=H^3/\Gamma$ the D=4 theory has an $AdS_4$ vacuum which uplifts to the
known supersymmetric $AdS_4\times H^3/\Gamma\times S^4$ 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 charged scalar fields, and another
instability involving neutral 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 $z\sim 39$.
