AdS_5 Solutions of Type IIB Supergravity and Generalized Complex Geometry

TL;DR

This paper employs generalized geometry to analyze supersymmetric AdS_5 solutions in type IIB supergravity, revealing their complex cone structures and linking geometric properties to dual SCFT characteristics.

Contribution

It introduces a generalized geometric framework for AdS_5 solutions, extending Calabi-Yau cones to generalized complex cones, and connects flux conditions to symplectic structures and physical quantities.

Findings

Generalized complex cone geometry extends Calabi-Yau cones.

Dilatation and R-symmetry vectors are generalized holomorphic.

Non-vanishing five-form flux implies a symplectic cone.

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.