Three-point Green function of the stress-energy tensor in the AdS/CFT correspondence

TL;DR

This paper calculates the three-point function of the stress-energy tensor in various conformal field theories using the AdS/CFT correspondence, confirming known results for certain theories and providing new data for others.

Contribution

It provides explicit computations of the stress-energy tensor 3-point function in d-dimensional CFTs via AdS gravity, including new results for strongly coupled theories.

Findings

Matching coefficients with free field results in d=4 for ${ m extbf{N}=4}$ SYM.

New 3-point function values for strongly coupled ${ m extbf{N}=8}$ superconformal scalar.

New 3-point function values for (2,0) tensor multiplet in d=6.

Abstract

We compute the 3-point function of the stress-energy tensor in the d-dimensional CFT from the AdS_{d+1} gravity. For d=4 the coefficients of the three linearly independent conformally covariant forms entering the 3-point function are exactly the same as given by the free field computations in the ${\cal N}=4$ SYM just as expected from the known renormalization theorems. For d=3 and d=6 our results give the value of the corresponding 3-point function in the theories of strongly coupled ${\cal N}=8$ superconformal scalar and (2,0) tensor multiplets respectively.