An Eight Loop Amplitude via Antipodal Duality

TL;DR

This paper presents an eight-loop computation of the six-particle MHV amplitude in planar ${\cal N}=4$ super-Yang-Mills theory, utilizing antipodal duality and recent form factor calculations, with extensive validation through various physical limits.

Contribution

It introduces a novel application of antipodal duality to compute high-loop amplitudes, reducing ambiguities and validating the duality at eight loops.

Findings

Successful eight-loop amplitude calculation using antipodal duality.

Amplitude passes multiple theoretical consistency checks.

Validation of antipodal duality at high loop order.

Abstract

We compute the six-particle maximally-helicity-violating (MHV) amplitude in planar ${\cal N}=4$ super-Yang-Mills theory at eight loops, using antipodal duality and the recently computed eight-loop three-point form factor for the chiral stress energy tensor multiplet. Antipodal duality maps the form factor symbol to the amplitude symbol on a two-dimensional parity-preserving surface in the three-dimensional amplitude kinematics. There are remarkably few ambiguities in lifting from two to three dimensions, nor in promoting the symbol to a function. The amplitude passes many tests, including near-collinear, multi-Regge, factorization, self-crossing and origin limits. These checks also constitute a validation of antipodal duality at eight loops.