AdS spacetimes from wrapped M5 branes

TL;DR

The authors present a unifying G-structure framework for a broad family of AdS_3, AdS_4, and AdS_5 spacetimes in M-theory by casting them as AdS limits of wrapped M5-brane geometries on calibrated cycles of special holonomy manifolds. They show how generalized calibrations encode the full set of supersymmetry conditions and demonstrate that known gauged-supergravity AdS solutions sit inside this general scheme. The work derives explicit AdS reductions for co-associative, associative, SLAG, and Kähler cycles, and provides new singular AdS_3/AdS_4 backgrounds, plus a Toda/LLM-type structure for certain AdS_5 limits. Overall, the paper advances a geometric, predictive program for classifying and constructing holographic duals of SCFTs arising from wrapped brane configurations, and connects calibrated geometry with AdS/CFT in a cohesive way.

Abstract

We derive a complete geometrical characterisation of a large class of $AdS_3$, $AdS_4$ and $AdS_5$ supersymmetric spacetimes in eleven-dimensional supergravity using G-structures. These are obtained as special cases of a class of supersymmetric $\mathbb{R}^{1,1}$, $\mathbb{R}^{1,2}$ and $\mathbb{R}^{1,3}$ geometries, naturally associated to M5-branes wrapping calibrated cycles in manifolds with $G_2$, SU(3) or SU(2) holonomy. Specifically, the latter class is defined by requiring that the Killing spinors satisfy the same set of projection conditions as for wrapped probe branes, and that there is no electric flux. We show how the R-symmetries of the dual field theories appear as isometries of the general AdS geometries. We also show how known solutions previously constructed in gauged supergravity satisfy our more general G-structure conditions, demonstrate that our conditions for half-BPS $AdS_5$ geometries are precisely those of Lin, Lunin and Maldacena, and construct some new singular solutions.