Instantons and non-renormalisation in AdS/CFT

The series of perturbative fluctuations around a multi-instanton contributi on to a specific class of correlation functions of supercurrents in N = 4 s upersymmetric SU(N) Yang-Mills theory is examined in the light of the AdS/C FT correspondence. Subject to certain plausible assumptions, we argue that a given term in the 1/N expansion in such a background receives only a fini te number of perturbative corrections in the 't Hooft limit. Such instanton non-renormalisation theorems would explain, for example, the exact agreeme nt of certain weak coupling Yang-Mills instanton calculations with the stro ng coupling predictions arising from D-instanton effects in string theory a mplitudes. These non-renormalisation theorems essentially follow from the a ssumption of a well defined derivative (alpha') expansion in the string the ory dual of the Yang-Mills theory.