Nilpotent invariants in N=4 SYM

Abstract It is shown that there are no nilpotent invariants in N =4 analytic superspace for n ≤4 points. It is argued that there is (at least) one such invariant for n =5 points which is not invariant under U (1) Y . The consequences of these results are that the n =2 and 3 point correlation functions of the N =4 gauge-invariant operators which correspond to KK multiplets in AdS supergravity are given exactly by their tree level expressions, the 4 point correlation functions of such operators are invariant under U (1) Y and correlation functions with n ≥4 points have non-trivial dependence on the Yang-Mills coupling constant.