Four-point functions of all-different-weight chiral primary operators in the supergravity approximation

TL;DR

This paper computes new four-point correlation functions of all-different-weight 1/2 BPS operators in N=4 SYM using supergravity, confirming a recent Mellin-space conjecture and advancing understanding of AdS/CFT correlators.

Contribution

It presents the first calculations of all-different-weight four-point functions and introduces simplified algorithms for supergravity computations, validating a Mellin-space conjecture.

Findings

Computed two new four-point functions with all-different weights.

Confirmed the validity of the recently conjectured Mellin-space formula.

Developed simplified computational methods for supergravity exchange calculations.

Abstract

Recently a Mellin-space formula was conjectured for the form of correlation functions of $1/2$ BPS operators in planar $\mathcal{N}=4$ SYM in the strong 't Hooft coupling limit. In this work we report on the computation of two previously unknown four-point functions of operators with weights $\langle 2345 \rangle$ and $\langle 3456\rangle$, from the effective type-IIB supergravity action using AdS/CFT. These correlators are novel: they are the first correlators with all-different weights and in particular $\langle 3456\rangle$ is the first next-next-next-to-extremal correlator to ever have been computed. We also present simplifications of the known algorithm, without which these computations could not have been executed without considerable computer power. The main simplifications we found are present in the computation of the exchange Lagrangian and in the computation of $a$ tensors. After bringing our results in the appropriate form we successfully corroborate the recently conjectured formula.