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

Gauntlett, Jerome P.; Martelli, Dario; Sparks, James; Waldram, Daniel

Classical Quantum Gravity 23, No. 14, 4693-4718 (2006).

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.

MSC:

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