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This paper analyzes the supersymmetric solutions to five and six-dimensional minimal (un)gauged supergravities for which the bilinear Killing vector constructed from the Killing spinor is null. We focus on the spacetimes which admit an…
Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence…
A Killing tensor field on a Riemannian space corresponds to an integral of the geodesic flow polynomial in momenta. A Killing tensor field is called decomposable if it is a polynomial in Killing vector fields. In this paper, we first prove…
We study the general requirement for supersymmetric AdS$_6$ solutions in type IIB supergravity. We employ the Killing spinor technique and study the differential and algebraic relations among various Killing spinor bilinears to find the…
We solve the Killing spinor equations of 6-dimensional (1,0) superconformal theories in all cases. In particular, we derive the conditions on the fields imposed by the Killing spinor equations and demonstrate that these depend on the…
We derive the necessary and sufficient conditions for the existence of a Killing spinor in N=(1,0) gauge supergravity in six dimensions coupled to a single tensor multiplet, vector multiplets and hypermultiplets. These are shown to imply…
The present work provides a mathematically rigorous account on super fiber bundle theory, connection forms and their parallel transport, that ties together various approaches. We begin with a detailed introduction to super fiber bundles. We…
We examine Killing spinor equations of the general IIB pp-wave backgrounds, which contain a scalar H(x^m,x^-) in the metric and a self-dual four-form \xi(x^m,x^-) in the self-dual five-form flux. Considering non-harmonic extra Killing…
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…
We study briefly some properties of real Clifford algebras and identify them as matrix algebras. We then show that the representation space on which Clifford algebras act are spinors and we study in details matrix representations. The…
We give an explicit description (in component fields) of a holomorphic theory associated to a general supersymmetric background of $\mathcal N=1$ supergravity in ten dimensions. Conjecturally, this provides a sought-for holomorphic…
The new 4D geometry whose Killing vectors span the Poincar\'e algebra is presented and its structure is analyzed. The new geometry can be regarded as the Poincar\'e-invariant solution of the degenerate extension of the vacuum Einstein field…
The correspondence between domain-wall and cosmological solutions of gravity coupled to scalar fields is explained. Any domain wall solution that admits a Killing spinor is shown to correspond to a cosmology that admits a pseudo-Killing…
We show that all IIB supergravity backgrounds which admit more than 28 Killing spinors are maximally supersymmetric. In particular, we find that for all N>28 backgrounds the supercovariant curvature vanishes, and that the quotients of…
We show that higher degree Dirac currents of twistor and Killing spinors correspond to the hidden symmetries of the background spacetime which are generalizations of conformal Killing and Killing vector fields respectively. They are the…
We test the robustness of the conditions required for the existence of (supersymmetric) warped flux anti-de Sitter, de Sitter, and Minkowski backgrounds in supergravity theories using as examples suitable foliations of anti-de Sitter…
We classify the geometry of all supersymmetric IIB backgrounds which admit the maximal number of $G$-invariant Killing spinors. For compact stability subgroups $G=G_2, SU(3)$ and SU(2), the spacetime is locally isometric to a product…
We analyze the localization equations relevant to the quantum entropy of spinning supersymmetric black holes in five-dimensional asymptotically flat space. The precise problem is to classify all solutions to the off-shell supersymmetry…
A pseudo-Riemannian Einstein manifold with a Killing spinor and Killing constant $\lambda$ induces on its nondegenerate hypersurfaces a pair of spinors $\phi,\psi$ and a symmetric tensor $A$, corresponding to the second fundamental form.…
We study supersymmetric AdS$_D$ backgrounds of eleven-dimensional or type II supergravity preserving $\mathcal{N}$ supersymmetries using generalised geometry. We show that a large class correspond precisely to spaces admitting a generalised…