Multi-Particle Amplitudes from the Four-Point Correlator in Planar N=4 SYM

TL;DR

This paper explores how the four-point correlator in planar N=4 super Yang-Mills theory encodes information about multi-particle scattering amplitudes, revealing a method to extract individual amplitudes using symmetry assumptions.

Contribution

It demonstrates that under Yangian symmetry and dual conformal basis assumptions, individual scattering amplitudes can be disentangled from the four-point correlator's integrand, up to seven points and two loops.

Findings

The four-point correlator integrand exhibits hidden permutation symmetry.

Assuming Yangian symmetry allows disentangling of amplitude contributions.

Method tested successfully up to seven points and two loops.

Abstract

A non-trivial consequence of the super-correlator/super-amplitude duality is that the integrand of the four-point correlation function of stress-tensor multiplets in planar N=4 super Yang-Mills contains a certain combination of n-point amplitude integrands for any n. This combination is the sum of products of all helicity super-amplitudes with their corresponding helicity conjugates. The four-point correlator itself is described by a single scalar function whose loop level integrands possess a hidden permutation symmetry facilitating its computation up to ten loops. We discover that assuming Yangian symmetry and an appropriate basis of planar dual conformal integrands it is possible to disentangle the contributions from the individual amplitudes from this combination. We test this up to seven points and up to two loops. This suggests that any scattering amplitude for any n, with any helicity structure and at any loop order may be extractable from the four-point correlator.