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

TL;DR

This paper calculates stress tensor correlators in free superconformal theories in 3 and 6 dimensions, revealing ratios consistent with supergravity predictions, thus supporting the AdS/CFT correspondence.

Contribution

It provides explicit computations of 2- and 3-point stress tensor correlators in free superconformal theories in d=3 and d=6, and compares them with supergravity results, highlighting non-trivial coefficient matches.

Findings

Ratios of 3-point to 2-point correlators match supergravity predictions.

Computed correlators differ from strong-coupling results by specific factors.

Results support the AdS/CFT correspondence in these theories.

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 3-point correlators for a single d=3 and d=6 multiplet differ from the "strong-coupling" AdS_4 and AdS_7 supergravity predictions by the factors $4\sqrt2 \over 3\pi}N^{3/2}$ and $4N^3$ respectively. These are the same factors as found earlier in hep-th/9703040 in the comparison of the brane free field theory and the 11-d supergravity predictions for the absorption cross-sections of longitudinally polarized gravitons by multiple 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-d supergravity on AdS_{d+1} x S^{10-d}.