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

Index theory and dynamical symmetry enhancement near IIB horizons

We show that the number of supersymmetries of IIB black hole horizons is N=2 N_- + 2 index(D_\lambda), where index(D_\lambda) is the index of the Dirac operator twisted with the line bundle \lambda^{1/2} of IIB scalars, and N_- is the dimension of the kernel of a horizon Dirac operator which depends on IIB fluxes. Therefore, all IIB horizons preserve an even number of supersymmetries. In addition if the horizons have non-trivial fluxes and N_- is nonzero, then index(D_\lambda) is non-negative, and the horizons admit an sl(2,R) symmetry subalgebra. This provides evidence that all such horizons have an AdS/CFT dual. Furthermore if the orbits of sl(2,R) are two-dimensional, the IIB horizons are warped products AdS_2 X S.Comment: 37 pages, late

Geometry of all supersymmetric four-dimensional N=1{\cal N}=1 supergravity backgrounds

We solve the Killing spinor equations of ${\cal N}=1$ supergravity, with four supercharges, coupled to any number of vector and scalar multiplets in all cases. We find that backgrounds with N=1 supersymmetry admit a null, integrable, Killing vector field. There are two classes of N=2 backgrounds. The spacetime in the first class admits a parallel null vector field and so it is a pp-wave. The spacetime of the other class admits three Killing vector fields, and a vector field that commutes with the three Killing directions. These backgrounds are of cohomogeneity one with homogenous sections either \bR^{2,1} or $AdS_3$ and have an interpretation as domain walls. The N=3 backgrounds are locally maximally supersymmetric. There are N=3 backgrounds which arise as discrete identifications of maximally supersymmetric ones. The maximally supersymmetric backgrounds are locally isometric to either \bR^{3,1} or $AdS_4$.Comment: 15 pages; minor changes, references added, published versio

M-theory backgrounds with 30 Killing spinors are maximally supersymmetric

We show that all M-theory backgrounds which admit more than 29 Killing spinors are maximally supersymmetric. In particular, we find that the supercovariant curvature of all backgrounds which preserve 30 supersymmetries, subject to field equations and Bianchi identities, vanishes, and that there are no such solutions which arise as discrete quotients of maximally supersymmetric backgrounds.Comment: 37 pages, latex. Minor changes

IIB black hole horizons with five-form flux and extended supersymmetry

We classify under some assumptions the IIB black hole horizons with 5-form flux preserving more than 2 supersymmetries. We find that the spatial horizon sections with non-vanishing flux preserving 4 supersymmetries are locally isometric either to S^1 * S^3 * T^4 or to S^1 * S^3 * K_3 and the associated near horizon geometries are locally isometric to AdS_3 * S^3 * T^4 and AdS_3 * S^3 * K_3$, respectively. The near horizon geometries preserving more than 4 supersymmetries are locally isometric to R^{1,1} * T^8.Comment: 16 pages, latex. Minor typos correcte

N=31 is not IIB

We adapt the spinorial geometry method to investigate supergravity backgrounds with near maximal number of supersymmetries. We then apply the formalism to show that the IIB supergravity backgrounds with 31 supersymmetries preserve an additional supersymmetry and so they are maximally supersymmetric. This rules out the existence of IIB supergravity preons.Comment: 7 page

All Killing Superalgebras for Warped AdS Backgrounds

We present all the symmetry superalgebras $\mathfrak{g}$ of all warped AdS$_k\times_w M^{d-k}$, $k>2$, flux backgrounds in $d=10, 11$ dimensions preserving any number of supersymmetries. First we give the conditions for $\mathfrak{g}$ to decompose into a direct sum of the isometry algebra of AdS$_k$ and that of the internal space $M^{d-k}$. Assuming this decomposition, we identify all symmetry superalgebras of AdS$_3$ backgrounds by showing that the isometry groups of internal spaces act transitively on spheres. We demonstrate that in type II and $d=11$ theories the AdS$_3$ symmetry superalgebras may not be simple and also present all symmetry superalgebras of heterotic AdS$_3$ backgrounds. Furthermore, we explicitly give the symmetry superalgebras of AdS$_k$, $k>3$, backgrounds and prove that they are all classical.Comment: 41 pages, late

IIB horizons

We solve the Killing spinor equations for all near-horizon IIB geometries which preserve at least one supersymmetry. We show that generic horizon sections are 8-dimensional almost Hermitian spin${}_c$ manifolds. Special cases include horizon sections with a $Spin(7)$ structure and those for which the Killing spinor is pure. We also explain how the common sector horizons and the horizons with only 5-form flux are included in our general analysis. We investigate several special cases mainly focusing on the horizons with constant scalars admitting a pure Killing spinor and find that some of these exhibit a generalization of the 2-SCYT condition that arises in the horizons with 5-form fluxes only. We use this to construct new examples of near-horizon geometries with both 3-form and 5-form fluxes.Comment: 27 page