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

References in corpus (7)

• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Conjectures for Large N Superconformal N=4 Chiral Primary Four Point Functions
• Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence
• High Energy Scattering in the AdS/CFT Correspondence
• Mellin representation of the graviton bulk-to-bulk propagator in AdS