Supersymmetric AdS\(_{5}\) solutions of type IIB supergravity. (English) Zbl 1096.83069

Summary: We analyse the most general bosonic supersymmetric solutions of type IIB supergravity whose metrics are warped products of five-dimensional anti-de Sitter space (AdS\(_{5}\)) with a five-dimensional Riemannian manifold \(M_{5}\). All fluxes are allowed 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 \(M_{5}\). For a special class, with constant dilaton and vanishing axion, we reduce the problem to solving a second-order nonlinear 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 giving complete metrics on \(S^{5}\) but with three-form flux and Killing spinors that are not globally defined.


83E50 Supergravity
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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