Nilpotent Invariants in N = 4 Sym

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.