Four-point functions of 1/2-BPS operators of any weights in the supergravity approximation

TL;DR

The paper addresses the problem of computing four-point functions of 1/2-BPS operators in planar $\mathcal{N}=4$ SYM at strong coupling and tests the Mellin-space conjecture of Rastelli et al. by leveraging a simplified supergravity algorithm together with the harmonic polynomial formalism. It implements these methods in Mathematica to compute all nontrivial connected correlators with weights up to $8$ (plus two very high-weight cases), generating a public database and validating the Mellin representation for the majority of cases. The results provide 94 correlators (including 64 new ones) and show agreement with the Mellin conjecture for 91 correlators (61 new), reinforcing the conjectured structure while significantly expanding the known data. This work offers a practical framework for rapid higher-weight computations and lays groundwork toward a general proof of the Mellin conjecture and deeper probes of AdS/CFT via Mellin space.

Abstract

We present the computation of all the correlators of 1/2-BPS operators in $\mathcal{N} = 4$ SYM with weights up to 8 as well as some very high-weight correlation functions from the effective supergravity action. The computation is done by implementing the recently developed simplified algorithm in combination with the harmonic polynomial formalism. We provide a database of these results attached to this publication and additionally check for almost all of the functions in this database that they agree with the conjecture on their Mellin-space form.