Instantons and non-renormalisation in AdS/CFT

The series of perturbative fluctuations around a multi-instanton contributionto 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/CFTcorrespondence. Subject to certain plausible assumptions, we argue that a giventerm in the 1/N expansion in such a background receives only a finite number ofperturbative corrections in the 't Hooft limit. Such instantonnon-renormalisation theorems would explain, for example, the exact agreement ofcertain weak coupling Yang-Mills instanton calculations with the strongcoupling predictions arising from D-instanton effects in string theoryamplitudes. These non-renormalisation theorems essentially follow from theassumption of a well defined derivative $(\alpha^{\prime})$ expansion in thestring theory dual of the Yang-Mills theory.Comment: 11 pages, harvmac, minor typo correcte