Folding Amplitudes into Form Factors: An Antipodal Duality.

Lance J Dixon,Ömer Gürdoğan,Matthias Wilhelm,Andrew J Mcleod

doi:10.1103/physrevlett.128.111602

Abstract

We observe that the three-gluon form factor of the chiral part of the stress-tensor multiplet in planar 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.

Highlights

We observe that the three-gluon form factor of the chiral part of the stress-tensor multiplet in planar N 1⁄4 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, which acts at symbol level by reversing the order of letters in each term
Introduction.—In the study of quantum field theory, we occasionally encounter dualities, or relations between seemingly unrelated quantities. One such example is the duality between scattering amplitudes and closed light-like polygonal Wilson loops in planar maximally supersymmetric Yang-Mills (N 1⁄4 4 SYM) theory [1–7], and its extension to a triality relating both quantities to a particular kinematic limit of correlation functions of the stress tensor supermultiplet [8–12]

Summary

Introduction

We observe that the three-gluon form factor of the chiral part of the stress-tensor multiplet in planar N 1⁄4 4 super-Yang-Mills theory is dual to the six-gluon MHV amplitude on its parity-preserving surface. Folding Amplitudes into Form Factors: An Antipodal Duality 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.

Results

Conclusion