String corrections to four point functions in the AdS/CFT correspondence

Abstract

In a string calculation to order α′ 3, we compute an eight-derivative four-dilaton term in the type IIB effective action. Following the AdS prescription, we compute the order ( g YM 2 N c ) −3/2 correction to the four-point correlation function involving the operator tr F 2 in four dimensional N=4 super Yang-Mills using the string corrected type IIB action extending the work of Freedman et al. (hep-th/9808006). In the limit where two of the Yang-Mills operators approach each other, we find that our correction to the four-point correlation functions develops a logarithmic singularity. We discuss the possible cancellation of this logarithmic singularities by conjecturing new terms in the type IIB effective action.