Folding Amplitudes into Form Factors: An Antipodal Duality

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.

5+2 pages, 2 figures, 2 tables. v2: added further checks at kinematic points, some clarifications and references; version to appear in PRL

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Cited by in corpus (17)

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• Three-point energy correlator in $\mathcal{N}=4$ super Yang-Mills Theory
• First look at the evaluation of three-loop non-planar Feynman diagrams for Higgs plus jet production
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Non-planar BCFW Grassmannian Geometries
• Antipodal Symmetry of Two-Loop MHV Amplitudes
• All Two-Loop Feynman Integrals for Five-Point One-Mass Scattering
• A Two-Loop Four-Point Form Factor at Function Level
• A high-precision result for a full-color three-loop three-point form factor in $\mathcal{N}=4$ SYM
• New relations for tree-level form factors and scattering amplitudes
• Antipodal self-duality of square fishnet graphs
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Generalized symmetries as homotopy Lie algebras