Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-06-22
Commun.Math.Phys.299:365-408,2010
Physics
High Energy Physics
High Energy Physics - Theory
56 pages; v2: minor changes, version to be published in Commun. Math. Phys
Scientific paper
10.1007/s00220-010-1083-y
We use the formalism of generalized geometry to study the generic supersymmetric AdS_5 solutions of type IIB supergravity that are dual to 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 Kahler-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.
Gabella Maxime
Gauntlett Jerome P.
Palti Eran
Sparks James
Waldram Daniel
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