IIB backgrounds with five-form flux Original Research Article

We investigate all image supersymmetric IIB supergravity backgrounds with non-vanishing five-form flux. The Killing spinors have stability subgroups image, image and image. In the image 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 image 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 image 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 image structure. The image backgrounds are pp-waves propagating in an eight-dimensional manifold with holonomy image. In addition we show that all the supersymmetric solutions of simple five-dimensional supergravity with a time-like Killing vector field, which include the image black holes, lift to image pure Killing spinor IIB backgrounds. We also show that the LLM solution is associated with a co-symplectic co-homogeneity one image manifold which has principal orbit image.