Near-extremal correlators and vanishing supergravity couplings in AdS/CFT

We study near-extremal n-point correlation functions of chiral primary oper ators, in which the maximal scale dimension k is related to the others by k = Sigma (i) k(i) - m with m less than or equal to n - 3. Through order g(2 ) in field theory, we show that these correlators are simple sums of terms each of which factors into products of lower-point correlators. Terms which contain only factors of two- and three-point functions are not renormalize d, but other terms have non-vanishing order g(2) corrections. We then show that the contributing AdS exchange diagrams neatly match this factored structure. Ln particular, for n = 4, 5 precise agreement in form a nd coefficient is established between supergravity and the non-renormalized factored terms from field theory. On the other hand, contact diagrams in s upergravity would produce a non-factored structure. This leads us to conjec ture that the corresponding bulk couplings vanish, so as to achieve full ag reement between the structure of these correlators in supergravity and weak -coupling field theory. (C) 2000 Elsevier Science B.V. All rights reserved.