Towards all loop supergravity amplitudes on AdS5×S5

Agnese Bissi,Giulia Fardelli,Alessandro Georgoudis

doi:10.1103/physrevd.104.l041901

Abstract

We study the four point function of the superconformal primary of the stress-tensor multiplet in four dimensional $\mathcal{N}=4$ Super Yang Mills, at large 't Hooft coupling and in a large $N$ expansion. This observable is holographically dual to four graviton amplitudes in type IIB supergravity on $AdS_5 \times S^5$. We construct the most trascendental piece of the correlator at order $N^{-6}$ and compare it with the flat space limit of the corresponding two loops amplitude. This comparison allows us to conjecture structures of the correlator/amplitude which should be present at any loop order.

Highlights

Since the advent of the AdS=conformal field theory (CFT) correspondence, the mapping between correlation functions of local gaugeinvariant operators and scattering amplitudes has been in the spotlight
We study the four-point function of the superconformal primary of the stress-tensor multiplet in fourdimensional N 1⁄4 4 super Yang-Mills theory, at strong coupling and in a large-N expansion
This observable is holographically dual to a four-graviton amplitude in type IIB supergravity on AdS5 × S5

Summary

INTRODUCTION

Since the advent of the AdS=CFT correspondence, the mapping between correlation functions of local gaugeinvariant operators and scattering amplitudes has been in the spotlight. In this paper we address the study of the four-point function of protected operators of dimension two in four-dimensional N 1⁄4 4 super Yang-Mills theory with SUðNÞ gauge group, at strong ’t Hooft coupling λ 1⁄4 g2N and as an expansion in inverse powers of N This quantity is holographically related to loop corrections of four-point graviton scattering amplitudes in the supergravity approximation in an AdS5 × S5 background. We find a relation between the CFT flat-space limit and iterated s-channel discontinuities of the amplitude We conjecture that this fact persists at any loop order and that we can predict certain analytic properties of ladder diagrams, using uniquely the constraints from leading- and subleading-order OPE data. In particular we conjecture that the same identification holds for the full AdS5 × S5 space

FOUR-POINT FUNCTION

Method

Flat space

AMPLITUDE

COMPARISON