A Universal Formula for the Stress-Tensor Contribution to Scalar Four-Point Functions

Abstract

We illustrate the power and efficiency of a recently uncovered Mellin-space approach to AdS/CFT correlation functions by providing a universal formula for the 4-scalar graviton-exchange Witten diagram, for arbitrary CFT-dual scaling dimensions. Our result keeps the space-time dimension generic as well, and is expressed as a combination of just 11 hypergeometric functions. Such hypergeometric functions are related to scalar-exchange diagrams. In particular, if reverse-engineered in terms of D-functions, this might be viewed as a first-step towards proving a long-standing conjecture by Dolan, Nirschl and Osborn pertaining to four-point correlators of chiral primary operators at strong coupling. Most importantly, the technology developed herein marks an additional development towards the long-anticipated computation of the four-point function of the N=4 sYM stress-tensor.

17 pages, 1 figure. Zipped source file includes a Mathematica notebook