Supersymmetric geometries of IIA supergravity I

IIA supergravity backgrounds preserving one supersymmetry locally admit four types of Killing spinors distinguished by the orbits of $Spin(9,1)$ on the space of spinors. We solve the Killing spinor equations of IIA supergravity with and without cosmological constant for Killing spinors representing two of these orbits, with isotropy groups $Spin(7)$ and $Spin(7)\ltimes\mathbb{R}^8$. In both cases, we identify the geometry of spacetime and express the fluxes in terms of the geometry. We find that the geometric constraints of backgrounds with a $Spin(7)\ltimes\mathbb{R}^8$ invariant Killing spinor are identical to those found for heterotic backgrounds preserving one supersymmetry.Comment: 21 page

Kappa symmetry, generalized calibrations and spinorial geometry

We extend the spinorial geometry techniques developed for the solution of supergravity Killing spinor equations to the kappa symmetry condition for supersymmetric brane probe configurations in any supergravity background. In particular, we construct the linear systems associated with the kappa symmetry projector of M- and type II branes acting on any Killing spinor. As an example, we show that static supersymmetric M2-brane configurations which admit a Killing spinor representing the SU(5) orbit of $Spin(10,1)$ are generalized almost hermitian calibrations and the embedding map is pseudo-holomorphic. We also present a bound for the Euclidean action of M- and type II branes embedded in a supersymmetric background with non-vanishing fluxes. This leads to an extension of the definition of generalized calibrations which allows for the presence of non-trivial Born-Infeld type of fields in the brane actions.Comment: 9 pages, latex, references added and minor change

Classification of IIB backgrounds with 28 supersymmetries

We show that all IIB backgrounds with strictly 28 supersymmetries are locally isometric to the plane wave solution of arXiv:hep-th/0206195. Moreover, we demonstrate that all solutions with more than 26 supersymmetries and only 5-form flux are maximally supersymmetric. The N=28 plane wave solution is a superposition of the maximally supersymmetric IIB plane wave with a heterotic string solution. We investigate the propagation of strings in this background, find the spectrum and give the string light-cone Hamiltonian.Comment: 30 pages, typos correcte

All null supersymmetric backgrounds of N=2, D=4 gauged supergravity coupled to abelian vector multiplets

The lightlike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. The solutions fall into two classes, depending on whether the Killing spinor is constant or not. In both cases, we give explicit examples of supersymmetric backgrounds. Among these BPS solutions, which preserve one quarter of the supersymmetry, there are gravitational waves propagating on domain walls or on bubbles of nothing that asymptote to AdS_4. Furthermore, we obtain the additional constraints obeyed by half-supersymmetric vacua. These are divided into four categories, that include bubbles of nothing which are asymptotically AdS_4, pp-waves on domain walls, AdS_3 x R, and spacetimes conformal to AdS_3 times an interval.Comment: 55 pages, uses JHEP3.cls. v2: Minor errors corrected, small changes in introductio

IIB backgrounds with five-form flux

We investigate all N=2 supersymmetric IIB supergravity backgrounds with non-vanishing five-form flux. The Killing spinors have stability subgroups Spin(7)\ltimes\bR^8, SU(4)\ltimes\bR^8 and $G_2$. In the SU(4)\ltimes\bR^8 case, two different types of geometry arise depending on whether the Killing spinors are generic or pure. In both cases, the backgrounds admit a null Killing vector field which leaves invariant the SU(4)\ltimes \bR^8 structure, and an almost complex structure in the directions transverse to the lightcone. In the generic case, the twist of the vector field is trivial but the almost complex structure is non-integrable, while in the pure case the twist is non-trivial but the almost complex structure is integrable and associated with a relatively balanced Hermitian structure. The $G_2$ backgrounds admit a time-like Killing vector field and two spacelike closed one-forms, and the seven directions transverse to these admit a co-symplectic $G_2$ structure. The Spin(7)\ltimes\bR^8 backgrounds are pp-waves propagating in an eight-dimensional manifold with holonomy $Spin(7)$. In addition we show that all the supersymmetric solutions of simple five-dimensional supergravity with a time-like Killing vector field, which include the $AdS_5$ black holes, lift to SU(4)\ltimes\bR^8 pure Killing spinor IIB backgrounds. We also show that the LLM solution is associated with a co-symplectic co-homogeneity one $G_2$ manifold which has principal orbit $S^3\times S^3$.Comment: 39 pages, typos corrected and references amende

IIB solutions with N>28 Killing spinors are maximally supersymmetric

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 maximally supersymmetric backgrounds either preserve all 32 or N<29 supersymmetries.Comment: 27 page