Four-point functions in the CFT-AdS correspondence

Abstract

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 $\mathrm{tr}{F}^{2}$ and $\mathrm{tr}{\mathrm{FF}}^{*}$ (``dilaton'' and ``axion'') operators in $\mathcal{N}=4$ supersymmetric $\mathrm{SU}(N)$ Yang-Mills theory as predicted by type-IIB supergravity in the five-dimensional AdS background.