M ar 2 00 8 IIB backgrounds with five - form flux

We investigate all N = 2 supersymmetric IIB supergravity backgrounds with non-vanishing five-form flux. The Killing spinors have stability subgroups Spin(7)⋉ R , SU(4) ⋉ R and G2. In the SU(4) ⋉ R 8 case, two different types of geometry arise depending on whether the Killing spinors are generic or pure. In both cases, the backgrounds admit a null Killing vector field which leaves invariant the SU(4) ⋉ R structure, and an almost complex structure in the directions transverse to the lightcone. In the generic case, the twist of the vector field is trivial but the almost complex structure is non-integrable, while in the pure case the twist is non-trivial but the almost complex structure is integrable and associated with a relatively balanced Hermitian structure. The G2 backgrounds admit a time-like Killing vector field and two spacelike closed one-forms, and the seven directions transverse to these admit a co-symplectic G2 structure. The Spin(7) ⋉ R 8 backgrounds are pp-waves propagating in an eight-dimensional manifold with holonomy Spin(7). In addition we show that all the supersymmetric solutions of simple fivedimensional supergravity with a time-like Killing vector field, which include the AdS5 black holes, lift to SU(4)⋉R 8 pure Killing spinor IIB backgrounds. We also show that the LLM solution is associated with a co-symplectic co-homogeneity one G2 manifold which has principal orbit S 3 × S3.