The exceptional generalised geometry of supersymmetric AdS flux backgrounds

TL;DR

This paper uses exceptional generalised geometry to analyze supersymmetric AdS flux backgrounds, revealing their structure, symmetries, and dual field theory quantities, including central charge and R-charge, with explicit examples in type IIB and M-theory.

Contribution

It introduces a framework describing AdS flux backgrounds with eight supercharges via generalised structures and explores their geometric and physical properties, including explicit examples and dual field theory relations.

Findings

Describes AdS flux backgrounds with exceptional generalised geometry.

Identifies a generalised Reeb vector encoding symmetries and charges.

Connects geometric structures to dual field theory quantities like central charge.

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.