Folding Amplitudes into Form Factors: An Antipodal Duality

TL;DR

This paper uncovers a duality between the three-gluon form factor and the six-gluon MHV amplitude in planar N=4 super-Yang-Mills theory, linked via an antipode operation on polylogarithms, supported by seven-loop evidence.

Contribution

It reveals a novel antipodal duality connecting form factors and amplitudes in N=4 SYM, expanding understanding of their mathematical structure.

Findings

Duality holds up to seven loops.

Map involves antipode operation on polylogarithms.

Supports deeper algebraic structure in gauge theory amplitudes.

Abstract

We observe that the three-gluon form factor of the chiral part of the stress-tensor multiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory is dual to the six-gluon MHV amplitude on its parity-preserving surface. Up to a simple variable substitution, the map between these two quantities is given by the antipode operation defined on polylogarithms (as part of their Hopf algebra structure), which acts at symbol level by reversing the order of letters in each term. We provide evidence for this duality through seven loops.