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

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 423πN3/2 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 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 11-dimensional supergravity on AdSd+1×S10−d .