Three-point correlators of stress tensors in maximally-supersymmetric conformal theories in d=3 and d=6

We consider free superconformal theories of N = 8 scalar multiplet in d = 3 and (2, 0) tensor multiplet in d = 6 and compute 2-point and 3-point correlators of their stress tensors. The results for the 2-point and the 3-point correlators for a single d = 3 and d = 6 multiplet differ from 4 root 2/3 pi N-3/2 and 4N(3) the "strong-coupling" AdS(4) and AdS(7) supergravity predictions by the factors respectively These are the same factors as found earlier in hep-th/9703040 in the comparison of the brane free field theory and the d = 11 supergravity predictions for the absorption cross sections of longitudinally polarized gravitons by N M2 and M5 branes. While the correspondence of the results for the cross sections and 2-point functions was expected on the basis of unitarity, the fact that the same coefficients appear in the ratio of the free-theory and supergravity 3-point functions is nontrivial. Thus, like in the d = 4 SYM case, in both d = 3 and d = 6 theories the ratio of the 3-point and 2-point correlators (TTT)/(TT) is exactly the same in the free field theory and in the interacting CFT as described (to leading order in large N) by the Ii-dimensional supergravity on AdS(d+1) x S10-d. (C) 2000 Elsevier Science B.V. All rights reserved.