Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps

TL;DR

This paper introduces new graphical relations in planar maximally supersymmetric Yang-Mills theory that, combined with existing rules, enable the calculation of four-point correlation functions and scattering amplitudes up to ten loops, advancing the understanding of high-loop order computations.

Contribution

The paper presents two novel graphical relations that, together with the rung rule, allow for the determination of amplitudes and correlators up to ten loops in planar maximally supersymmetric Yang-Mills theory.

Findings

Full ten-loop amplitude and correlator expressions provided.

Derived rules significantly reduce computational complexity.

Survey of features of nine and ten loop expressions included.

Abstract

We introduce two new graphical-level relations among possible contributions to the four-point correlation function and scattering amplitude in planar, maximally supersymmetric Yang-Mills theory. When combined with the rung rule, these prove powerful enough to fully determine both functions through ten loops. This then also yields the full five-point amplitude to eight loops and the parity-even part to nine loops. We derive these rules, illustrate their applications, compare their relative strengths for fixing coefficients, and survey some of the features of the previously unknown nine and ten loop expressions. Explicit formulae for amplitudes and correlators through ten loops are available at: http://goo.gl/JH0yEc.