AdS 5 Solutions of Type IIB Supergravity and Generalized Complex Geometry
AdS 5 Solutions of Type IIB Supergravity and Generalized Complex Geometry
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AdS 5 IIB型超重力与广义复几何解
DOI：
10.1007/s00220-010-1083-y
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发表时间：
2010
影响因子：
2.4
通讯作者：
Gabella M
中科院分区：
文献类型：
--
作者：
Gabella M
利用广义几何的形式论，研究了IIB型超重力的一般超对称ad5解，它们是对超共形场论（SCFTs） ind= 4的对偶。这样的解有一个相关的六维广义复锥几何，它是Calabi-Yau锥几何的扩展。对对偶SCFT的扩张和r对称进行了对偶，并证明了它们在锥上是广义全纯的。我们将圆锥体广义化约为一个横向四维空间，并证明这也是一个广义复几何，它是Kähler-Einstein几何的扩展。值得注意的是，如果五型通量不消失，则锥是辛的。利用辛结构可以得到对偶SCFT的中心电荷的Duistermaat-Heckman型积分和对偶到BPS缠绕的d3膜的算子的共形维数。我们使用Pilch-Warner解决方案来说明这些结果。
We use the formalism of generalized geometry to study the generic supersymmetricAdS5solutions of type IIB supergravity that are dual tosuperconformal field theories (SCFTs) ind= 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 andR-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.