AdS$\times$S Mellin Bootstrap, Hidden 10d Symmetry and Five-point Kaluza-Klein Functions in $\mathcal{N}=4$ SYM

TL;DR

This paper introduces a novel AdS×S factorization approach in Mellin space for correlators in $ ext{AdS}_5 imes ext{S}^5$ supergravity, enabling unified computation of five-point and four-point correlators in $ ext{N}=4$ SYM.

Contribution

It develops a new AdS×S factorization formula for correlator generating functions and applies it within Mellin space bootstrap, revealing a hidden 10d symmetry and simplifying multi-point calculations.

Findings

Unified formulas for five-point half-BPS correlators

Unified formulas for four-point correlators with superdescendants

Applicable to generic multi-point tree-level computations

Abstract

We propose an AdS$\times$S factorization formula at the level of the generating function for correlators with arbitrary Kaluza-Klein configurations, and implement it in the supergravity limit of $\mathcal{N}=4$ super Yang-Mills. By incorporating this mechanism into Mellin space bootstrap, together with an observed $Z_2$ symmetry under AdS$\ \leftrightarrow\ $S, we manage to simultaneously work out unified formulas both for all five-point half-BPS correlators and for all four-point correlators with one superdescendant. This AdS\times$S bootstrap method is directly applicable to generic multi-point computation at tree level.