An Eight Loop Amplitude via Antipodal Duality

Abstract

We compute the six-particle maximally-helicity-violating (MHV) amplitude in planar $\mathcal{N}=4$ 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.

Comments: 50 pages, 3 figures, 6 tables, 8 loops