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arXiv · hep-th/9906151

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

Hong Liu·A. A. Tseytlin
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Abstract

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 ϕand massive `fixed' scalar νin 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 ϕϕνcoupling 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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Hong Liu, A. A. Tseytlin. 1999-07-02. Dilaton - fixed scalar correlators and AdS_5 x S^5 - SYM correspondence. https://doi.org/10.1088/1126-6708%2F1999%2F10%2F003

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