  In this paper we study the n-point correlation functions of two different
families of local gauge invariant operators in N=4 supersymmetric Yang-Mills
theory. The main idea is to consider the correlation functions of operators
which all share a number of supersymmetries irrespective of their relative
locations. We achieve this by equipping the operators with explicit space-time
dependence. We provide evidence by different methods that these n-point
correlators do not receive quantum corrections in perturbation theory and are
hence given exactly by their tree-level result. The arguments rely on explicit
checks for general four-point correlators, some five-point and six-point
correlators and a more abstract calculation based on a novel topological
twisting of N=4 supersymmetric Yang-Mills theory.
