Wrapped M5-branes, consistent truncations and AdS/CMT

TL;DR

This paper constructs consistent truncations of D=11 supergravity on specific 3-manifolds, leading to new AdS and Lifshitz solutions, and explores their implications for dual 3D field theories, including black holes and instabilities.

Contribution

It provides the first consistent Kaluza-Klein reduction of D=11 supergravity on these manifolds, revealing new solutions and dual field theory phenomena.

Findings

Constructed D=11 black hole solutions with superconducting instabilities.

Found a Lifshitz solution with dynamical exponent z~39.

Established a link between supergravity reductions and 3D SCFTs.

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 $AdS_4$ 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 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 $z\sim 39$.