Type IIB flux compactifications on twistor bundles

We construct a U(1)U(1) bundle over N(1,1)N(1,1), usually considered as an SO(3)SO(3) bundle on CP2CP2, and show that type IIB supergravity can be consistently compactified over it. With the five form flux turned on, there is a solution for which the metric becomes Einstein. We further turn on 3-form fluxes and show that there is a one parameter family of solutions. In particular, there is a limiting solution of large 3-form fluxes for which two U(1)U(1) fiber directions of the metric shrink to zero size. We also discuss compactifications over N(1,1)N(1,1) to AdS3AdS3. All solutions turn out to be non-supersymmetric.