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Spacetime Singularity Resolution by M-Theory Fivebranes: Calibrated Geometry, Anti-de Sitter Solutions and Special Holonomy Metrics

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Abstract

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: Kähler 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 G 2 manifolds; complex lagrangian four-cycles in Sp(2) manifolds; and Cayley four-cycles in 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 G 2 metrics on an \({\mathbb{R}^4}\) bundle over S 3, and an \({\mathbb{R}^3}\) bundle over S 4 or \({\mathbb{CP}^2}\) ; the Calabi hyper-Kähler metric on \({T^*\mathbb{CP}^2}\) ; and the Bryant-Salamon-Gibbons-Page-Pope Spin(7) metric on an \({\mathbb{R}^4}\) bundle over S 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.

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Authors and Affiliations

  1. Theoretical Physics Group, Blackett Laboratory, Imperial College London, London, SW7 2AZ, U.K.

    Oisín A. P. Mac Conamhna

  2. The Institute for Mathematical Sciences, Imperial College London, London, SW7 2PE, U.K.

    Oisín A. P. Mac Conamhna

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Communicated by G.W. Gibbons

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Conamhna, O.A.P.M. Spacetime Singularity Resolution by M-Theory Fivebranes: Calibrated Geometry, Anti-de Sitter Solutions and Special Holonomy Metrics. Commun. Math. Phys. 284, 345–389 (2008). https://doi.org/10.1007/s00220-008-0570-x

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