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

In a string calculation to order ${\alpha }^{\mathrm{\prime }3}$, we compute an eight-derivative four-dilaton term in the type IIB effective action. Following the AdS prescription, we compute the order $(g_{YM}^2{N}_c{)}^{-3\mathrm{/}2}$ 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.