All loop structures in Supergravity Amplitudes on $Ad{S}_5\times S^5$ from CFT

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 $Ad{S}_5\times S^5$.

43 pages, Ancillary files contains various results presented in the paper. V2: Corrected typos, added references and modified figure. V3: reformatted for J.Phys. A, accepted version