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 iib supergravity and m-theory. in particular, we give the complete analysis of the generic ads5 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 $$ mathrm{mathcal{f}} $$ -maximisation) is encoded.