An eight loop amplitude via antipodal duality
Lance J. Dixon, Yu-Ting Liu
Abstract
A bstract We compute the six-particle maximally-helicity-violating (MHV) amplitude in planar $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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.