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

Abstract

We address the question of AdS/CFT correspondence in the case of the 3-point function <O_4 O_4 O_8>. 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 <O_4 O_4 O_8> 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 <O_4 O_4 O_8> correlator on the supergravity side.