Open AccessThe Volume of some Non-spherical Horizons and the AdS/CFT Correspondence
Author(s) -
Aaron Bergman,
Christopher P. Herzog
Publication year - 2002
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2002/01/030
Subject(s) - physics , supergravity , central charge , affine transformation , embedding , holomorphic function , einstein , mathematical physics , pure mathematics , magnetic monopole , theoretical physics , conformal map , supersymmetry , quantum mechanics , mathematical analysis , mathematics , artificial intelligence , computer science
We calculate the volumes of a large class of Einstein manifolds, namelySasaki-Einstein manifolds which are the bases of Ricci-flat affine conesdescribed by polynomial embedding relations in C^n. These volumes are importantbecause they allow us to extend and test the AdS/CFT correspondence. We usethese volumes to extend the central charge calculation of Gubser (1998) to thegeneralized conifolds of Gubser, Shatashvili, and Nekrasov (1999). Thesevolumes also allow one to quantize precisely the D-brane flux of the AdSsupergravity solution. We end by demonstrating a relationship between thevolumes of these Einstein spaces and the number of holomorphic polynomials(which correspond to chiral primary operators in the field theory dual) on thecorresponding affine cone.Comment: 25 pp, LaTeX, 1 figure, v2: refs adde
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