Supersymmetric AdS backgrounds and weak generalised holonomy

Abstract

We study supersymmetric AdS${}_D$ backgrounds of eleven-dimensional or type II supergravity preserving $\mathcal{N}$ supersymmetries using generalised geometry. We show that a large class correspond precisely to spaces admitting a generalised $G_{D,\mathcal{N}}$ structure with a weak integrability condition, which we call "weak generalised holonomy". This class contains all such backgrounds with odd $D$, but for even $D$ we must impose a technical assumption concerning the inner products of Killing spinors. It is known that all compact smooth solutions are included, though our analysis is purely local. We show that the Killing superalgebras of such backgrounds are isomorphic to the standard $\mathcal{N}$-extended AdS${}_D$ superalgebras, and give a geometric proof of the existence of isometries of the internal spaces which realise the AdS R-symmetry, as often assumed in explicit studies of such solutions.

19 pages

References in corpus (8)

• Generalised Geometry for M-Theory
• Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions
• AdS_6 solutions of type II supergravity
• Half-maximal supersymmetry from exceptional field theory
• Supersymmetric Backgrounds, the Killing Superalgebra, and Generalised Special Holonomy
• AdS_4 compactifications of AdS_7 solutions in type II supergravity
• New gaugings and non-geometry
• On supersymmetric Anti-de-Sitter, de-Sitter and Minkowski flux backgrounds

Cited by in corpus (1)

• All superalgebras for warped AdS${}_2$ and black hole near horizon geometries