All loop structures in Supergravity Amplitudes on $AdS_5 \times S^5$ from CFT

TL;DR

This paper computes specific structures in four-point functions of protected operators in N=4 Super Yang Mills, connecting them to supergravity amplitudes in AdS space and providing insights into their loop structures.

Contribution

It introduces a method to determine amplitude structures from leading order CFT data and relates them to supergravity amplitudes on AdS_5 x S^5.

Findings

Structures determined by leading order CFT data at all orders in large N expansion

Connection established between CFT structures and supergravity s-cut iterated amplitudes

Conjecture that the interpretation extends to supergravity on AdS_5 x S^5

Abstract

We computed a set of structures which appear in the four-point function of protected operators of dimension two in $\mathcal{N}=4$ Super Yang Mills with $SU(N)$ gauge group, at any order in a large $N$ expansion. They are determined only by leading order CFT data. By focusing on a specific limit, we made connection with the dual supergravity amplitude in flat space, where such structures correspond to iterated $s$-cuts. We made several checks and we conjecture that the same interpretation holds for supergravity amplitudes on $AdS_5 \times S^5$.