Supersymmetric AdS 5 solutions of M - theory

We analyse the most general supersymmetric solutions of D = 11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M6, with four-form flux on M6. We show that M6 is partly specified by a one-parameter family of four-dimensional Kähler metrics. We find a large family of new explicit regular solutions where M6 is a compact, complex manifold which is topologically a two-sphere bundle over a four-dimensional base, where the latter is either (i) Kähler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T /Z2. Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space. ∗ On leave from: Blackett Laboratory, Imperial College, London, SW7 2BZ, U.K.