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 M 6 , with 4-form flux on M 6 . We show that M 6 is partly specified by a one-parameter family of four-dimensional Kähler metrics. We find a large family of new explicit regular solutions where M 6 is a compact, complex manifold which is topologically a 2-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 . Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.