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Geometries with Killing Spinors and Supersymmetric AdS Solutions

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Abstract

The seven and nine dimensional geometries associated with certain classes of supersymmetric AdS 3 and AdS 2 solutions of type IIB and D = 11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further elucidate their properties and also generalise them to higher odd dimensions by introducing a new class of complex geometries in 2n + 2 dimensions, specified by a Riemannian metric, a scalar field and a closed three-form, which admit a particular kind of Killing spinor. In particular, for n ≥ 3, we show that when the geometry in 2n + 2 dimensions is a cone we obtain a class of geometries in 2n + 1 dimensions, specified by a Riemannian metric, a scalar field and a closed two-form, which includes the seven and nine-dimensional geometries mentioned above when n = 3, 4, respectively. We also consider various ansätze for the geometries and construct infinite classes of explicit examples for all n.

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Authors and Affiliations

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

    Jerome P. Gauntlett

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

    Jerome P. Gauntlett

  3. Department of Physics and Research Institute of Basic Science, Kyung Hee University, Seoul, 130-701, Korea

    Nakwoo Kim

Authors
  1. Jerome P. Gauntlett
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  2. Nakwoo Kim
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Correspondence to Jerome P. Gauntlett.

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Communicated by G.W. Gibbons

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Gauntlett, J.P., Kim, N. Geometries with Killing Spinors and Supersymmetric AdS Solutions. Commun. Math. Phys. 284, 897–918 (2008). https://doi.org/10.1007/s00220-008-0575-5

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  • DOI: https://doi.org/10.1007/s00220-008-0575-5

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