On Four-point Functions in the CFT/AdS Correspondence

We discuss the properties of four-point functions in the context of the correspondence between a classical supergravity theory in the bulk of the Anti de Sitter (AdS) space and quantum conformal field theory (CFT) at the boundary. The contribution to a four-point function from the exchange of a scalar field of arbitrary mass in AdS space is explicitly identified with that of the corresponding operator in the conformal partial wave expansion of a four-point function on the CFT side. Integral representations are found for the massless vector and graviton exchanges. We also discuss some aspects of the four-point functions of trF 2 and trFF ∗ (‘dilaton’ and ‘axion’) operators in the N = 4 supersymmetric SU(N) Yang-Mills theory as predicted by type IIB supergravity in the AdS5 background. July 1998 ∗ e-mail address: [email protected] ⋆ e-mail address: [email protected] † Also at Lebedev Physics Institute, Moscow.