The exceptional generalised geometry of supersymmetric AdS flux backgrounds

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 HB 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 F-maximisation) is encoded.