Nilpotent invariants in N=4 SYM

It is shown that there are no nilpotent invariants in N = 4 analytic superspace for n less than or equal to 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 greater than or equal to 4 points have non-trivial dependence on the Yang-Mills coupling constant. (C) 1999 Published by Elsevier Science B.V. All rights reserved.