On Four-point Functions in the CFT/AdS Correspondence

TL;DR

This paper explores the properties of four-point functions in the AdS/CFT correspondence, explicitly relating bulk scalar exchanges to boundary conformal partial waves, and discusses vector and graviton exchanges in the context of N=4 SYM.

Contribution

It provides explicit integral representations for massless vector and graviton exchanges and clarifies the correspondence between bulk scalar exchanges and boundary conformal partial waves.

Findings

Explicit identification of scalar exchange contributions with conformal partial waves.

Integral representations for vector and graviton exchange processes.

Insights into four-point functions of operators in N=4 supersymmetric Yang-Mills.

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 space and quantum conformal field theory 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 Tr F^2 and Tr F F^* (`dilaton' and `axion') operators in the N =4 supersymmetric Yang-Mills.