AdS_5 Solutions of Type IIB Supergravity and Generalized Complex Geometry
Abstract
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.
Cite
@article{arxiv.0906.4109,
title = {AdS_5 Solutions of Type IIB Supergravity and Generalized Complex Geometry},
author = {Maxime Gabella and Jerome P. Gauntlett and Eran Palti and James Sparks and Daniel Waldram},
journal= {arXiv preprint arXiv:0906.4109},
year = {2010}
}
Comments
56 pages; v2: minor changes, version to be published in Commun. Math. Phys