Instantons and Non-renormalisation in AdS/CFT

TL;DR

This paper explores how instanton effects in N=4 super Yang-Mills theory are protected from infinite perturbative corrections due to non-renormalisation theorems, supporting the consistency of AdS/CFT correspondence.

Contribution

It proposes non-renormalisation theorems for instanton contributions in N=4 SYM within the AdS/CFT framework, explaining exact weak- and strong-coupling agreement.

Findings

Finite perturbative corrections to instanton terms in 1/N expansion.

Support for non-renormalisation theorems in super Yang-Mills theory.

Consistency between weak coupling instanton calculations and string theory predictions.

Abstract

The series of perturbative fluctuations around a multi-instanton contribution to a specific class of correlation functions of supercurrents in $\cal N=4$ supersymmetric SU(N) Yang-Mills theory is examined in the light of the AdS/CFT correspondence. Subject to certain plausible assumptions, we argue that a given term in the 1/N expansion in such a background receives only a finite number of perturbative corrections in the 't Hooft limit. Such instanton non-renormalisation theorems would explain, for example, the exact agreement of certain weak coupling Yang-Mills instanton calculations with the strong coupling predictions arising from D-instanton effects in string theory amplitudes. These non-renormalisation theorems essentially follow from the assumption of a well defined derivative $(\alpha^{\prime})$ expansion in the string theory dual of the Yang-Mills theory.