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

Abstract

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 the ?strong-coupling? AdS4 and AdS7 supergravity predictions by the factors 4p2 3 N3/2 and 4N3 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 non-trivial. 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 11-dimensional supergravity on AdSd+1 ? S10?d.