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.

arXiv comment5+2 pages, 2 figures, 2 tables. v2: added further checks at kinematic points, some clarifications and references; version to appear in PRL

References in corpus (58)

• Harmonic Polylogarithms
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Comments on gluon scattering amplitudes via AdS/CFT
• From polygons and symbols to polylogarithmic functions
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• PolyLogTools - Polylogs for the masses
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Thermodynamic Bubble Ansatz
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• Y-system for Scattering Amplitudes
• Bootstrapping an NMHV amplitude through three loops
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Form factors at strong coupling via a Y-system
• Two-Loop QCD Corrections to the Helicity Amplitudes for $H\to$ 3 partons
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Hexagon functions and the three-loop remainder function
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• Dressing and Wrapping
• From correlation functions to Wilson loops
• The super-correlator/super-amplitude duality: Part I
• From correlation functions to scattering amplitudes
• Pulling the straps of polygons
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Analytic two-loop form factors in N=4 SYM
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• Cluster adjacency properties of scattering amplitudes
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• More on the duality correlators/amplitudes
• OPE for all Helicity Amplitudes
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Cluster algebras for Feynman integrals
• The super-correlator/super-amplitude duality: Part II
• A Three-Point Form Factor Through Five Loops
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• Nonsinglet pentagons and NMHV amplitudes
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Fermionic pentagons and NMHV hexagon
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• An Operator Product Expansion for Form Factors
• Dual conformal invariance for form factors
• Matrix pentagons
• A simple collinear limit of scattering amplitudes at strong coupling
• All orders results for self-crossing Wilson loops mimicking double parton scattering

Cited by in corpus (17)

• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Antipodal Self-Duality for a Four-Particle Form Factor
• 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