# The geometry of the AdS/CFT correspondence

### APA

Sparks, J. (2009). The geometry of the AdS/CFT correspondence. Perimeter Institute. https://pirsa.org/08050063

### MLA

Sparks, James. The geometry of the AdS/CFT correspondence. Perimeter Institute, May. 08, 2009, https://pirsa.org/08050063

### BibTex

@misc{ pirsa_PIRSA:08050063, doi = {10.48660/08050063}, url = {https://pirsa.org/08050063}, author = {Sparks, James}, keywords = {}, language = {en}, title = {The geometry of the AdS/CFT correspondence}, publisher = {Perimeter Institute}, year = {2009}, month = {may}, note = {PIRSA:08050063 see, \url{https://pirsa.org}} }

**Collection**

Talk Type

Abstract

I will describe how the geometry of supersymmetric AdS solutions of type IIB string theory may be rephrased in terms of the geometry of generalized (in the sense of Hitchin) Calabi-Yau cones. Calabi-Yau cones, and hence Sasaki-Einstein manifolds, are a special case, and thus the geometrical structure described may be considered a form of generalized Sasaki-Einstein geometry. Generalized complex geometry naturally describes many features of the AdS/CFT correspondence. For example, a certain type changing locus is identified naturally with the moduli space of the dual CFT. There is also a generalized Reeb vector field, which defines a foliation with a transverse generalized Hermitian structure. For solutions with non-zero D3-brane charge, the generalized Calabi-Yau cone is also equipped with a canonical symplectic structure, and this captures many quantities of physical interest, such as the central charge and conformal dimensions of certain operators, in the form of Duistermaat-Heckman type integrals.