(Non-)perturbative tests of the AdS/CFT correspondence

TL;DR

This paper reviews perturbative and non-perturbative tests of the AdS/CFT correspondence, focusing on correlation functions, instantons, and non-renormalization properties in N=4 SYM theory.

Contribution

It provides a comprehensive summary of field theory tests of holography, including instanton dualities and non-renormalization theorems for correlation functions.

Findings

Confirmation of D-instanton and YM instanton duality

Non-renormalization of two- and three-point functions of CPOs

Partial non-renormalization of four-point functions

Abstract

I summarize perturbative and non-perturbative field theory tests of the holographic correspondence between type IIB superstring on AdS_5xS^5 and N=4 SYM theory. The holographic duality between D-instantons and YM instantons is briefly described. Non renormalization of two- and three-point functions of CPO's and their extremal and next-to-extremal correlators are then reviewed. Finally, partial non-renormalization of four-point functions of lowest CPO's is analyzed in view of the interpretation of short distance logarithmic behaviours in terms of anomalous dimensions of unprotected operators.