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

TL;DR

This work extends the AdS/CFT correspondence by analyzing instanton-induced correlation functions in ${\cal N}=4$ $SU(N)$ Yang–Mills theory at large $N$, incorporating the full set of fermionic moduli from SU(2) embeddings. It develops the one-instanton measure, operator profiles, and scalar propagators in the instanton background, and computes non-minimal correlators that involve Kaluza–Klein excitations, showing how these YM results map to D-instanton and higher-derivative interactions in type IIB string theory on AdS$_5\times S^5$. The analysis reveals that reproducing AdS amplitudes requires combining D-instanton induced vertices with classical bulk interactions, and that the $1/N$ expansion of YM instanton effects encodes the structure of higher-derivative terms like $\alpha'^{-1}$ and beyond in the IIB effective action. The results provide evidence that the KK tower and non-minimal couplings are encoded systematically in YM correlators, supporting the view that large-$N$ instanton physics probes the full derivative expansion of the string theory dual. The study also discusses near-extremal and anti-instanton contributions, highlighting cancellations and ambiguities that point to rich, testable structure in the non-perturbative regime of AdS/CFT.

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.