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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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