Wrapped M5-branes, consistent truncations and AdS/CMT

TL;DR

This paper develops a new, fully consistent Kaluza–Klein reduction of D=11 supergravity on \Sigma_3 × S^4, yielding the bosonic sector of a four-dimensional N=2 gauged supergravity with a single vector multiplet and two hypermultiplets, whose scalars parametrize SU(1,1)/U(1) × G_{2(2)}/SO(4). For Σ_3 = H^3/Γ, the 4D theory admits an AdS_4 vacuum that uplifts to AdS_4 × H^3/Γ × S^4 and describes the N=2 SCFT on wrapped M5-branes; this setup is used to construct D=11 black holes at finite temperature and chemical potential and to analyze instabilities leading to holographic superconductivity and neutral-hair phases, as well as a Lifshitz solution with z ≈ 39. The work provides two distinct AdS_4 vacua (one supersymmetric, one non-supersymmetric) and identifies a rich spectrum of dual operators organized into OSp(2|4) multiplets, with many operators irrelevant in the dual CFT. Furthermore, a Lifshitz Lif$_4(z)$ solution is found within a simplified truncation, highlighting the potential of top-down constructions to explore AdS/CMT phenomena in wrapped M5-brane theories.

Abstract

At the level of the bosonic fields, we construct consistent Kaluza--Klein reductions of D=11 supergravity on $Σ_3\times S^4$, where $Σ_3=H^3/Γ,S^3/Γ$ or $R^3/Γ$ where $Γ$ 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 $Σ_3=H^3/Γ$ the D=4 theory has an $AdS_4$ vacuum which uplifts to the known supersymmetric $AdS_4\times H^3/Γ\times S^4$ solution of D=11 supergravity that describes the N=2 $d=3$ SCFT arising when M5-branes wrap SLag 3-cycles $H^3/Γ$ in Calabi-Yau three-folds. We use the KK reduction for $Σ_3=H^3/Γ$ 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 $z\sim 39$.