Instanton-induced Yang-Mills correlation functions at large N and their AdS_5xS^5 duals

TL;DR

This paper analyzes instanton effects in N=4 SU(N) Yang-Mills theory at large N, matching these effects with D-instanton contributions in type IIB string theory via AdS/CFT, including higher derivative interactions and multi-fermion correlations.

Contribution

It extends previous instanton calculations by including additional fermionic moduli, enabling detailed matching with string theory D-instanton effects and higher derivative interactions.

Findings

Matching of instanton contributions with D-instanton effects in string theory.

Identification of higher derivative interactions in the IIB effective action.

Analysis of multi-fermion correlation functions consistent with supersymmetry.

Abstract

Correlation functions of chiral primary operators and their superconformal descendants in the N=4 supersymmetric SU(N) Yang-Mills theory are studied in detail in a one-instanton background and at large N. Whereas earlier calculations were restricted to correlation functions that are saturated by the 16 exact superconformal fermionic moduli, here the effect of the set of additional fermionic moduli associated with the embeddings of the SU(2) instanton in SU(N) is considered. The presence of the extra fermionic modes is essential for matching Yang-Mills instanton effects in various correlation functions with D-instanton effects in type IIB string theory via the AdS/CFT conjecture. The leading terms of this kind on the string side contribute at order 1/(alpha'), which is the same order as the R^4 interaction. For example, the instanton contributions to correlation functions of higher dimensional chiral primary operators are seen to match amplitudes involving Kaluza-Klein excitations of the supergravity fields, as expected. Another example is the matching of certain multi-fermion correlation functions which correspond to certain multi-fermion interactions required by supersymmetry of the IIB string effective action. Careful analysis of a variety of competing effects makes it possible to decipher contributions corresponding to higher derivative interactions in the IIB effective action. In this manner it is possible to check for the presence of terms of order alpha'. Comments are also made on the structure of instanton contributions to near-extremal correlation functions of chiral primary operators.