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AdS5 Solutions of Type IIB Supergravity and Generalized Complex Geometry

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Abstract

We use the formalism of generalized geometry to study the generic supersymmetric AdS 5 solutions of type IIB supergravity that are dual to \({\mathcal{N}=1}\) superconformal field theories (SCFTs) in d = 4. Such solutions have an associated six-dimensional generalized complex cone geometry that is an extension of Calabi-Yau cone geometry. We identify generalized vector fields dual to the dilatation and R-symmetry of the dual SCFT and show that they are generalized holomorphic on the cone. We carry out a generalized reduction of the cone to a transverse four-dimensional space and show that this is also a generalized complex geometry, which is an extension of Kähler-Einstein geometry. Remarkably, provided the five-form flux is non-vanishing, the cone is symplectic. The symplectic structure can be used to obtain Duistermaat-Heckman type integrals for the central charge of the dual SCFT and the conformal dimensions of operators dual to BPS wrapped D3-branes. We illustrate these results using the Pilch-Warner solution.

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Authors and Affiliations

  1. Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, U.K.

    Maxime Gabella & Eran Palti

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

    Jerome P. Gauntlett & Daniel Waldram

  3. Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB, U.K.

    Jerome P. Gauntlett & Daniel Waldram

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

    James Sparks

Authors
  1. Maxime Gabella
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  2. Jerome P. Gauntlett
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  3. Eran Palti
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  4. James Sparks
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  5. Daniel Waldram
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Correspondence to James Sparks.

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Communicated by A. Kapustin

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Gabella, M., Gauntlett, J.P., Palti, E. et al. AdS5 Solutions of Type IIB Supergravity and Generalized Complex Geometry. Commun. Math. Phys. 299, 365–408 (2010). https://doi.org/10.1007/s00220-010-1083-y

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  • DOI: https://doi.org/10.1007/s00220-010-1083-y

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