Supersymmetric AdS5 Solutions of Type IIB Supergravity

We analyse the most general bosonic supersymmetric solutions of type IIB supergravity whose metrics are warped products of five-dimensional anti-de Sitter space (AdS5) with a five-dimensional Riemannian manifold M5. All fluxes are allowed to be non-vanishing consistent with SO(4, 2) symmetry. We show that the necessary and sufficient conditions can be phrased in terms of a local identity structure on M5. For a special class, with constant dilaton and vanishing axion, we reduce the problem to solving a second order non-linear ODE. We find an exact solution of the ODE which reproduces a solution first found by Pilch and Warner. A numerical analysis of the ODE reveals an additional class of local solutions.