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

TL;DR

This work computes the 3-point function of the stress-energy tensor in a d-dimensional CFT via AdS_{d+1} gravity, carefully including boundary terms and performing the calculation at cubic order. The authors employ a covariant de Donder gauge to evaluate the on-shell bulk action, obtaining a conformally covariant structure with five tensor components and explicit coefficients A,...,E. In d=4, the results reproduce the free-field ${ cal N}=4$ SYM values up to the overall coupling, supporting non-renormalization of these correlators at strong coupling; for d=3 and d=6 they provide the corresponding strongly coupled values for the ${ cal N}=8$ SCFT and the (2,0) tensor multiplet, respectively, aligning AdS/CFT predictions across dimensions. The paper thus offers a nontrivial test of AdS/CFT by matching holographic results to known free-field results in four dimensions and supplying new strong-coupling data in other dimensions.

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.