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

TL;DR

This paper demonstrates that AdS5 x S5 remains a solution in type IIB supergravity even with non-perturbative higher-derivative corrections, and explores the implications for correlation functions and instantons in dual supersymmetric Yang-Mills theory.

Contribution

It shows the stability of AdS5 x S5 under non-perturbative corrections and derives exact results for graviton interactions, linking these to non-perturbative aspects of supersymmetric Yang-Mills theory.

Findings

AdS5 x S5 remains a solution with non-perturbative corrections.

Graviton two- and three-point functions are not renormalized.

Provides non-perturbative insights into instantons in gauge theory.

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.