Some systematics of the coupling constant dependence of N=4 Yang-Mills -: art. no. 045

The operator, O-tau, that generates infinitesimal changes of the coupling constant in N = 4 Yang-Mills sits in the same supermultiplet as the superconformal currents. We show how superconformal current Ward identities determine a class of terms in the operator product expansion of O-tau with any other operator. In certain cases, this leads to constraints on the coupling dependence of correlation functions in N = 4 Yang-Mills. As an application, we demonstrate the exact non-renormalization of two and certain three-point correlation functions of BPS operators.