All purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified. The solutions preserve either one half or all of the supersymmetry. Explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally supersymmetric analogue of the Gödel universe which lifts to a solution of eleven dimensional supergravity that preserves 20 supersymmetries.

We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on S 2 × S 3 of both quasi-regular and irregular type. These give rise to new solutions of type IIB supergravity which are expected to be dual to N = 1 superconformal field theories in four dimensions with compact or non-compact R-symmetry and rational or irrational central charges, respectively.

We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form Ê 1,9−d × M d , in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-structures and provide a comprehensive classification of static supersymmetric backgrounds in these theories. Generalised calibrations naturally appear since the geometries always admit NS or type I/heterotic fivebranes wrapping calibrated cycles.Some new solutions are presented. In particular we find d = 6 examples with a fibred structure which preserve N = 1, 2, 3 supersymmetry in type II and include compact type I/heterotic geometries.

We propose a way to classify the local form of all bosonic supersymmetric configurations of D=11 supergravity, using the differential forms that can be constructed as bi-linears from the Killing spinors. We show that the most general bosonic geometries either have a privileged SU(5) or a (Spin(7) ⋉ R 8 ) × R structure, depending on whether the Killing vector constructed from the Killing spinor is timelike or null, respectively. In the time-like case we derive the general local form of the geometry and show that it is almost completely determined by a certain SU(5) structure on the ten-dimensional space orthogonal to the orbits of the Killing vector.We also deduce what further conditions must be imposed in order that the equations of motion are satisfied. We illustrate the formalism with some known solutions and also present some new solutions including a rotating generalisation of the resolved membrane solutions and generalisations of the recently constructed D=11 Gödel solution. We also prove some general vanishing theorems for compactifications with flux.

We consider dilaton gravity theories in four spacetime dimensions parametrised by a constant a, which controls the dilaton coupling, and construct new exact solutions. We first generalise the C-metric of Einstein-Maxwell theory (a = 0) to solutions corresponding to oppositely charged dilaton black holes undergoing uniform acceleration for general a.We next develop a solution generating technique which allows us to "embed" the dilaton C-metrics in magnetic dilaton Melvin backgrounds, thus generalising the Ernst metric of Einstein-Maxwell theory. By adjusting the parameters appropriately, it is possible to eliminate the nodal singularities of the dilaton C-metrics. For a < 1 (but not for a ≥ 1), it is possible to further restrict the parameters so that the dilaton Ernst solutions have a smooth euclidean section with topology S 2 × S 2 − {pt}, corresponding to instantons * Address from 1st Oct. 1993: Relativity Group Department of Physics, University of California, Santa Barbara, CA 93106.describing the pair production of dilaton black holes in a magnetic field. A different restriction on the parameters leads to smooth instantons for all values of a with topology

We introduce a new framework for constructing black hole solutions that are holographically dual to strongly coupled field theories with explicitly broken translation invariance. Using a classical gravitational theory with a continuous global symmetry leads to constructions that involve solving ODEs instead of PDEs. We study in detail D = 4 Einstein-Maxwell theory coupled to a complex scalar field with a simple mass term. We construct black holes dual to metallic phases which exhibit a Drude-type peak in the optical conductivity, but there is no evidence of an intermediate scaling that has been reported in other holographic lattice constructions. We also construct black holes dual to insulating phases which exhibit a suppression of spectral weight at low frequencies. We show that the model also admits a novel AdS 3 × R solution.

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We analyse the geometrical structure of supersymmetric solutions of type II supergravity of the form R 1,9−n ×M n with non-trivial NS flux and dilaton.Solutions of this type arise naturally as the near-horizon limits of wrapped NS fivebrane geometries. We concentrate on the case d = 7, preserving two or four supersymmetries, corresponding to branes wrapped on associative or SLAG three-cycles. Given the existence of Killing spinors, we show that M 7 admits a G 2 -structure or an SU(3)-structure, respectively, of specific type. We also prove the converse result. We use the existence of these geometric structures as a new technique to derive some known and new explicit solutions, as well as a simple theorem implying that we have vanishing NS three-form and constant dilaton whenever M 7 is compact with no boundary. The analysis extends simply to other type II examples and also to type I supergravity.