Non-perturbative Effects in AdS5 * S5 String Theory and d=4 SUSY Yang--Mills

Abstract

We show that five-dimensional anti de-Sitter space remains a solution to low-energy type IIB supergravity when the leading higher-derivative corrections to the classical supergravity (which are non-perturbative in the string coupling) are included. Furthermore, at this order in the low energy expansion of the IIB theory the graviton two-point and three-point functions in $AdS_5 \times S^5$ are shown not to be renormalized and a precise expression is obtained for the four-graviton and related S-matrix elements. By invoking Maldacena's conjectured connection between IIB superstring theory and supersymmetric Yang--Mills theory corresponding statements are obtained concerning correlation functions of the energy-momentum tensor and related operators in the large-N Yang--Mills theory. This leads to interesting non-perturbative statements and insights into the r\^ole of instantons in the gauge theory.