Dilaton - fixed scalar correlators and AdS_5 x S^5 - SYM correspondence

Details Dilaton - fixed scalar correlators and AdS_5 x S^5 - SYM correspondence Dilaton - fixed scalar correlators and AdS_5 x S^5 - SYM correspondence

1999-06-18

arxiv.org/abs/hep-th/9906151v3

JHEP 9910:003,1999

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, harvmac; references added

Scientific paper

10.1088/1126-6708/1999/10/003

We address the question of AdS/CFT correspondence in the case of the 3-point function . O_4 and O_8 are particular primary states represented by F^2 + ... and F^4 + ... operators in \N=4 SYM theory and dilaton \phi and massive `fixed' scalar \nu in D=5 supergravity. While the value of computed in large N weakly coupled SYM theory is non-vanishing, the D=5 action of type IIB supergravity compactified on S^5 does not contain \phi\phi\nu coupling and thus the corresponding correlator seems to vanish on the AdS_5 side. This is in obvious contradiction with arguments suggesting non-renormalization of 2- and 3-point functions of states from short multiplets and implying agreement between the supergravity and SYM expressions for them. We propose a natural resolution of this paradox which emphasizes the 10-dimensional nature of the correspondence. The basic idea is to treat the constant mode of the dilaton as a part of the full S^5 Kaluza-Klein family of dilaton modes. This leads to a non-zero result for the correlator on the supergravity side.

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