The Volume of some Non-spherical Horizons and the AdS/CFT Correspondence

Details The Volume of some Non-spherical Horizons and the AdS/CFT Correspondence The Volume of some Non-spherical Horizons and the AdS/CFT Correspondence

2001-08-04

arxiv.org/abs/hep-th/0108020v2

JHEP 0201 (2002) 030

Physics

High Energy Physics

High Energy Physics - Theory

25 pp, LaTeX, 1 figure, v2: refs added

Scientific paper

10.1088/1126-6708/2002/01/030

We calculate the volumes of a large class of Einstein manifolds, namely Sasaki-Einstein manifolds which are the bases of Ricci-flat affine cones described by polynomial embedding relations in C^n. These volumes are important because they allow us to extend and test the AdS/CFT correspondence. We use these volumes to extend the central charge calculation of Gubser (1998) to the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999). These volumes also allow one to quantize precisely the D-brane flux of the AdS supergravity solution. We end by demonstrating a relationship between the volumes of these Einstein spaces and the number of holomorphic polynomials (which correspond to chiral primary operators in the field theory dual) on the corresponding affine cone.

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