Kaluza-Klein Five-Point Functions from $\textrm{AdS}_5\times S_5$ Supergravity

TL;DR

This paper advances the bootstrap approach to compute five-point correlation functions in IIB supergravity on AdS_5×S^5, introducing an efficient Mellin space method for higher Kaluza-Klein modes.

Contribution

It develops a new algorithm within Mellin space that simplifies the calculation of higher Kaluza-Klein five-point functions in holographic supergravity.

Findings

Closed-form five-point functions for ⟨pp222⟩ correlators.

Explicit results for spinning four-point functions of higher Kaluza-Klein modes.

Enhanced computational efficiency for holographic correlators.

Abstract

We continue to explore the bootstrap approach to five-point correlation functions for IIB supergravity on $AdS_5\times S^5$. Building on the result of [1], we develop an improved algorithm that allows us to more efficiently compute correlators of higher Kaluza-Klein modes. The new method uses only factorization and a superconformal twist, and is entirely within Mellin space where the analytic structure of holographic correlators is simpler. Using this method, we obtain in a closed form all five-point functions of the form $\langle pp222\rangle$, extending the earlier result for $p=2$. As a byproduct of our analysis, we also obtain explicit results for spinning four-point functions of higher Kaluza-Klein modes.