More on correlators and contact terms in N=4 SYM at order g(4)

We compute two-point functions of chiral operators Tr Phi (k) for any k, in N = 4 supersymmetric SU(N) Yang-Mills theory. We find that up to the order g(4) the perturbative corrections to the correlators vanish for all N. The cancellation occurs in a highly non trivial way, due to a complicated inte rplay between planar and non planar diagrams. In complete generality we sho w that this same result is valid for any simple gauge group. Contact term c ontributions signal the presence of ultraviolet divergences. They are arbit rary at the tree level, but the absence of perturbative renormalization in the non singular part of the correlators allows to compute them unambiguous ly at higher orders. In the spirit of the AdS/CFT correspondence we comment on their relation to infrared singularities in the supergravity sector. (C ) 2001 Elsevier Science B.V. All rights: reserved.