arXiv subjects
Publications and source records attributed to Wafic Sabra.
We construct a new class of solutions to the dispersionless hyper--CR equation, and show how any solution to this equation gives rise to a supersymmetric Einstein--Maxwell cosmological space--time in $(3+1)$--dimensions.
We show that a class of solutions of minimal supergravity in five dimensions is given by lifts of three--dimensional Einstein--Weyl structures of hyper-CR type. We characterise this class as most general near--horizon limits of supersymmetric solutions to the five--dimensional theory. In particular, we deduce that a compact spatial section of a horizon can only be a Berger sphere, a product metric on $S^1\times S^2$ or a flat three-torus. We then consider the problem of reconstructing all supersymmetric solutions from a given near--horizon geometry. By exploiting the ellipticity of the linearised field equations we demonstrate that the moduli space of transverse infinitesimal deformations of a near--horizon geometry is finite--dimensional.
We dimensionally reduce the bosonic sector of 10D Euclidean type IIA supergravity over a Calabi-Yau three-fold. The resulting theory describes the bosonic sector of 4D, N = 2 Euclidean supergravity coupled to vector- and hyper-multiplets. We show that the scalar target manifold of the vector-multiplets is projective special para-Kahler, and is therefore of split signature, whereas the target manifold of the hyper-multiplets is (positive-definite) quaternionic Kahler.
We show how to lift solutions of Euclidean Einstein-Maxwell equations with non-zero cosmological constant to solutions of eleven-dimensional supergravity theory with non-zero fluxes. This yields a class of 11D metrics given in terms of solutions to $SU(\infty)$ Toda equation. We give one example of a regular solution and analyse its supersymmetry. We also analyse the integrability conditions of the Killing spinor equations of N=2 minimal gauged supergravity in four Euclidean dimensions. We obtain necessary conditions for the existence of additional Killing spinors, corresponding to enhancement of supersymmetry. If the Weyl tensor is anti-self-dual then the supersymmetric metrics satisfying these conditions are given by separable solutions to the $SU(\infty)$ Toda equation. Otherwise they are ambi-Kähler and are conformally equivalent to Kähler metrics of Calabi type or to product metrics on two Riemann surfaces.
In AdS/CFT, the holographic Weyl anomaly computation relates the a-anomaly coefficient to the properties of the bulk action at the UV fixed point. This universal behavior suggests the possibility of a holographic c-theorem for the a-anomaly under flows to the IR. We prove such a c-theorem for higher curvature Lovelock gravity, where the bulk equations of motion remain second order. We also explore f(R) gravity as a toy model where higher derivatives cannot be avoided. In this case, monoticity of the flow requires an additional condition related to the higher derivative nature of the theory. This is in contrast to the case of f(R) black hole entropy, where the second law follows from application of the full Einstein equations and the null energy condition.
We classify super-symmetric solutions of the minimal $N=2$ gauged Euclidean supergravity in four dimensions. The solutions with anti-self-dual Maxwell field give rise to anti-self-dual Einstein metrics given in terms of solutions to the $SU(\infty)$ Toda equation and more general three-dimensional Einstein--Weyl structures. Euclidean Kastor--Traschen metrics are also characterised by the existence of a certain super covariantly constant spinor.
We discuss the relation between solutions admitting Killing spinors of minimal supergravities in five dimensions and four dimensional complex geometries. In the ungauged case (vanishing cosmological constant Λ=0) the solutions are determined in terms of a hyper-Kahler base space; in the gauged case (Λ<0) the complex geometry is Kahler; in the de Sitter case (Λ>0) the complex geometry is hyper-Kahler with torsion (HKT). In the latter case some details of the derivation are given. The method for constructing explicit solutions is discussed in each case.
We classify half-supersymmetric solutions of gauged N=2, D=5 supergravity coupled to an arbitrary number of abelian vector multiplets for which all of the Killing spinors generate null Killing vectors. We show that there are four classes of solutions, and in each class we find the metric, scalars and gauge field strengths. When the scalar manifold is symmetric, the solutions correspond to a class of local near horizon geometries recently found by Kunduri and Lucietti.
Solutions of five dimensional minimal de Sitter supergravity admitting Killing spinors are considered. It is shown that the "timelike'' solutions are determined in terms of a four dimensional hyper-Kahler torsion (HKT) manifold. If the HKT manifold is conformally hyper-Kahler the most general solution can be obtained from a sub-class of supersymmetric solutions of minimal N=2 ungauged supergravity, by means of a simple transformation. Examples include a multi-BMPV de Sitter solution, describing multiple rotating black holes co-moving with the expansion of the universe. If the HKT manifold is not conformally hyper-Kahler, examples admitting a tri-holomorphic Killing vector field are constructed in terms of certain solutions of three dimensional Einstein-Weyl geometry.
We prove the existence of 3/4-BPS preons in four- and five-dimensional gauged supergravities by explicitly constructing them as smooth quotients of the AdS_4 and AdS_5 maximally supersymmetric backgrounds, respectively. This result illustrates how the spacetime topology resurrects a fraction of supersymmetry previously ruled out by the local analysis of the Killing spinor equations.
We examine supersymmetric solutions of N=2, D=5 gauged supergravity coupled to an arbitrary number of abelian vector multiplets using the spinorial geometry method. By making use of methods developed in hep-th/0606049 to analyse preons in type IIB supergravity, we show that there are no solutions preserving exactly 3/4 of the supersymmetry.
In hep-th/0409174, Lin, Lunin and Maldacena constructed a set of regular 1/2 BPS geometries in IIB theory. These remarkable `bubbling AdS' geometries have a natural interpretation as duals of chiral primary operators with weight Delta=J in N=4 super-Yang Mills theory. Although these geometries have been assumed to be complete, from a purely supergravity point of view, additional 1/2 BPS configurations may potentially exist with a preferred null isometry. We explore this possibility and prove that the only additional class of 1/2 BPS solutions with SO(4) x SO(4) isometry are the familiar IIB pp-waves.
The classification of 1/4-supersymmetric solutions of five dimensional gauged supergravity coupled to arbitrary many abelian vector multiplets, which was initiated in hep-th/0401129, is completed. The structure of all solutions for which the Killing vector constructed from the Killing spinor is null is investigated in both the gauged and the ungauged theories and some new solutions are constructed.
We construct time dependent S-brane solutions in gauged and ungauged supergravities in various dimensions. The supergravity solutions we find are all special cases of solutions in gauged supergravities with symmetric potentials. We discuss some properties of these solutions and their relation to topological black holes in anti-de Sitter spaces.
We classify maximally supersymmetric backgrounds (vacua) of chiral (1,0) and (2,0) supergravities in six dimensions and, by reduction, also those of the minimal N=2 supergravity in five dimensions. Up to R-symmetry, the (2,0) vacua are in one-to-one correspondence with (1,0) vacua, and these in turn are locally isometric to Lie groups admitting a bi-invariant lorentzian metric with anti-selfdual parallelising torsion, which we classify. We then show that the five-dimensional vacua are homogeneous spaces arising canonically as the spaces of right cosets of spacelike one-parameter subgroups.
Instanton and wormhole solutions are constructed in a d-dimensional gravity theory with an axion-dilaton pair of scalar fields. We discuss the cases of vanishing, positive and negative cosmological constant.