33 research outputs found

    The geometry of extended null supersymmetry in M-theory

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    For supersymmetric spacetimes in eleven dimensions admitting a null Killing spinor, a set of explicit necessary and sufficient conditions for the existence of any number of arbitrary additional Killing spinors is derived. The necessary and sufficient conditions are comprised of algebraic relationships, linear in the spinorial components, between the spinorial components and their first derivatives, and the components of the spin connection and four-form. The integrability conditions for the Killing spinor equation are also analysed in detail, to determine which components of the field equations are implied by arbitrary additional supersymmetries and the four-form Bianchi identity. This provides a complete formalism for the systematic and exhaustive investigation of all spacetimes with extended null supersymmetry in eleven dimensions. The formalism is employed to show that the general bosonic solution of eleven dimensional supergravity admitting a G2G_2 structure defined by four Killing spinors is either locally the direct product of R1,3\mathbb{R}^{1,3} with a seven-manifold of G2G_2 holonomy, or locally the Freund-Rubin direct product of AdS4AdS_4 with a seven-manifold of weak G2G_2 holonomy. In addition, all supersymmetric spacetimes admitting a (G2⋉R7)×R2(G_2\ltimes\mathbb{R}^7)\times\mathbb{R}^2 structure are classified.Comment: 36 pages, latex; v2, section classifying all spacetimes admitting a (G2⋉R7)×R2(G_2\ltimes\mathbb{R}^7)\times\mathbb{R}^2 structure included; v3, typos corrected. Final version to appear in Phys.Rev.

    Inverting geometric transitions: explicit Calabi-Yau metrics for the Maldacena-Nunez solutions

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    Explicit Calabi-Yau metrics are derived that are argued to map to the Maldacena-Nu\~{n}ez AdS solutions of M-theory and IIB under geometric transitions. In each case the metrics are singular where a H^2 K\"{a}hler two-cycle degenerates but are otherwise smooth. They are derived as the most general Calabi-Yau solutions of an ansatz for the supergravity description of branes wrapped on K\"{a}hler two-cycles. The ansatz is inspired by re-writing the AdS solutions, and the structure defined by half their Killing spinors, in this form. The world-volume theories of fractional branes wrapped at the singularities of these metrics are proposed as the duals of the AdS solutions. The existence of supergravity solutions interpolating between the AdSAdS and Calabi-Yau metrics is conjectured and their boundary conditions briefly discussed.Comment: 1+17 pages, LaTeX; v2, typos corrected; v3, typos corrected, final versio

    Supersymmetric AdS_3 solutions of type IIB supergravity

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    For every positively curved Kahler-Einstein manifold in four dimensions we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of AdS_3 with a compact seven-dimensional manifold and have non-vanishing five-form flux. Via the AdS/CFT correspondence, the solutions are dual to two-dimensional conformal field theories with (2,0) supersymmetry. The corresponding central charges are rational numbers.Comment: Dedicated to Rafael Sorkin in celebration of his 60th birthday; 5 pages, latex. v2, typos corrected, to appear in PR

    AdS spacetimes from wrapped D3-branes

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    We derive a geometrical characterisation of a large class of AdS_3 and AdS_2 supersymmetric spacetimes in IIB supergravity with non-vanishing five-form flux using G-structures. These are obtained as special cases of a class of supersymmetric spacetimes with an R1,1\mathbb{R}^{1,1} or R\mathbb{R} (time) factor that are associated with D3-branes wrapping calibrated 2- or 3- cycles, respectively, in manifolds with SU(2), SU(3), SU(4) and G_2 holonomy. We show how two explicit AdS solutions, previously constructed in gauged supergravity, satisfy our more general G-structure conditions. For each explicit solution we also derive a special holonomy metric which, although singular, has an appropriate calibrated cycle. After analytic continuation, some of the classes of AdS spacetimes give rise to known classes of BPS bubble solutions with R×SO(4)×SO(4)\mathbb{R}\times SO(4)\times SO(4), R×SO(4)×U(1)\mathbb{R}\times SO(4)\times U(1), and R×SO(4)\mathbb{R}\times SO(4) symmetry. These have 1/2, 1/4 and 1/8 supersymmetry, respectively. We present a new class of 1/8 BPS geometries with R×SU(2)\mathbb{R}\times SU(2) symmetry, obtained by analytic continuation of the class of AdS spacetimes associated with D3-branes wrapped on associative three-cycles.Comment: 1+30 pages; v2, references added; v3, typos corrected, reference adde

    AdS spacetimes from wrapped M5 branes

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    We derive a complete geometrical characterisation of a large class of AdS3AdS_3, AdS4AdS_4 and AdS5AdS_5 supersymmetric spacetimes in eleven-dimensional supergravity using G-structures. These are obtained as special cases of a class of supersymmetric R1,1\mathbb{R}^{1,1}, R1,2\mathbb{R}^{1,2} and R1,3\mathbb{R}^{1,3} geometries, naturally associated to M5-branes wrapping calibrated cycles in manifolds with G2G_2, SU(3) or SU(2) holonomy. Specifically, the latter class is defined by requiring that the Killing spinors satisfy the same set of projection conditions as for wrapped probe branes, and that there is no electric flux. We show how the R-symmetries of the dual field theories appear as isometries of the general AdS geometries. We also show how known solutions previously constructed in gauged supergravity satisfy our more general G-structure conditions, demonstrate that our conditions for half-BPS AdS5AdS_5 geometries are precisely those of Lin, Lunin and Maldacena, and construct some new singular solutions.Comment: 1+56 pages, LaTeX; v2, references added; v3, minor corrections, final version to appear in JHE

    Spacetime singularity resolution by M-theory fivebranes: calibrated geometry, Anti-de Sitter solutions and special holonomy metrics

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    The supergravity description of various configurations of supersymmetric M-fivebranes wrapped on calibrated cycles of special holonomy manifolds is studied. The description is provided by solutions of eleven-dimensional supergravity which interpolate smoothly between a special holonomy manifold and an event horizon with Anti-de Sitter geometry. For known examples of Anti-de Sitter solutions, the associated special holonomy metric is derived. One explicit Anti-de Sitter solution of M-theory is so treated for fivebranes wrapping each of the following cycles: K\"{a}hler cycles in Calabi-Yau two-, three- and four-folds; special lagrangian cycles in three- and four-folds; associative three- and co-associative four-cycles in G2G_2 manifolds; complex lagrangian four-cycles in Sp(2)Sp(2) manifolds; and Cayley four-cycles in Spin(7)Spin(7) manifolds. In each case, the associated special holonomy metric is singular, and is a hyperbolic analogue of a known metric. The analogous known metrics are respectively: Eguchi-Hanson, the resolved conifold and the four-fold resolved conifold; the deformed conifold, and the Stenzel four-fold metric; the Bryant-Salamon-Gibbons-Page-Pope G2G_2 metrics on an R4\mathbb{R}^4 bundle over S3S^3, and an R3\mathbb{R}^3 bundle over S4S^4 or CP2\mathbb{CP}^2; the Calabi hyper-K\"{a}hler metric on T∗CP2T^*\mathbb{CP}^2; and the Bryant-Salamon-Gibbons-Page-Pope Spin(7)Spin(7) metric on an R4\mathbb{R}^4 bundle over S4S^4. By the AdS/CFT correspondence, a conformal field theory is associated to each of the new singular special holonomy metrics, and defines the quantum gravitational physics of the resolution of their singularities.Comment: 1+52 page

    The general form of supersymmetric solutions of N=(1,0) U(1) and SU(2) gauged supergravities in six dimensions

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    We obtain necessary and sufficient conditions for a supersymmetric field configuration in the N=(1,0) U(1) or SU(2) gauged supergravities in six dimensions, and impose the field equations on this general ansatz. It is found that any supersymmetric solution is associated to an SU(2)⋉R4SU(2)\ltimes \mathbb{R}^4 structure. The structure is characterized by a null Killing vector which induces a natural 2+4 split of the six dimensional spacetime. A suitable combination of the field equations implies that the scalar curvature of the four dimensional Riemannian part, referred to as the base, obeys a second order differential equation. Bosonic fluxes introduce torsion terms that deform the SU(2)⋉R4SU(2)\ltimes\mathbb{R}^4 structure away from a covariantly constant one. The most general structure can be classified in terms of its intrinsic torsion. For a large class of solutions the gauge field strengths admit a simple geometrical interpretation: in the U(1) theory the base is K\"{a}hler, and the gauge field strength is the Ricci form; in the SU(2) theory, the gauge field strengths are identified with the curvatures of the left hand spin bundle of the base. We employ our general ansatz to construct new supersymmetric solutions; we show that the U(1) theory admits a symmetric Cahen-Wallach4×S2_4\times S^2 solution together with a compactifying pp-wave. The SU(2) theory admits a black string, whose near horizon limit is AdS3×S3AdS_3\times S_3. We also obtain the Yang-Mills analogue of the Salam-Sezgin solution of the U(1) theory, namely R1,2×S3R^{1,2}\times S^3, where the S3S^3 is supported by a sphaleron. Finally we obtain the additional constraints implied by enhanced supersymmetry, and discuss Penrose limits in the theories.Comment: 1+29 pages, late
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