The exceptional generalised geometry of supersymmetric AdS flux backgrounds

Abstract

We analyse generic AdS flux backgrounds preserving eight supercharges in $D=4$ and $D=5$ dimensions using exceptional generalised geometry. We show that they are described by a pair of globally defined, generalised structures, identical to those that appear for flat flux backgrounds but with different integrability conditions. We give a number of explicit examples of such "exceptional Sasaki-Einstein" backgrounds in type IIB supergravity and M-theory. In particular, we give the complete analysis of the generic AdS${}_5$ M-theory backgrounds. We also briefly discuss the structure of the moduli space of solutions. In all cases, one structure defines a "generalised Reeb vector" that generates a Killing symmetry of the background corresponding to the R-symmetry of the dual field theory, and in addition encodes the generic contact structures that appear in the $D=4$ M-theory and $D=5$ type IIB cases. Finally, we investigate the relation between generalised structures and quantities in the dual field theory, showing that the central charge and R-charge of BPS wrapped-brane states are both encoded by the generalised Reeb vector, as well as discussing how volume minimisation (the dual of $a$- and $\mathcal{F}$-maximisation) is encoded.

40 pages

References in corpus (9)

• Generalised Geometry for M-Theory
• Sasaki-Einstein Manifolds and Volume Minimisation
• Generalized Geometry and M theory
• HyperKahler and quaternionic Kahler manifolds with S^1-symmetries
• Classes of AdS4 type IIA/IIB compactifications with SU(3)xSU(3) structure
• Gravity duals to deformed SYM theories and Generalized Complex Geometry
• Supersymmetric Vacua in N=2 Supergravity
• The central charge of supersymmetric AdS_5 solutions of type IIB supergravity
• Generalized geometric vacua with eight supercharges

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• 7-dimensional $\mathcal{N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory
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• Heterotic backgrounds via generalised geometry: moment maps and moduli
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry
• The higher-dimensional origin of five-dimensional $\mathcal{N}=2$ gauged supergravities
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• A geometric formulation of exceptional field theory
• Infinite and finite consistent truncations on deformed generalised parallelisations
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