A note on interactions of (non-commutative) instantons via AdS/CFT

We consider the interaction between instantons and anti-instantons in four-dimensional N=4 super-Yang–Mills theory at large N and large ʹt Hooft coupling, as described by D-instantons via AdS/CFT duality. We give an estimate of the strength of the interaction in various regimes. We also discuss the case of non-commutative super-Yang–Mills theory where the interaction between instantons and anti-instantons can be used as a way to probe the locality properties of the theory in the supergravity picture, without explicit reference to the definition of local operators.