Antipodal Self-Duality for a Four-Particle Form Factor

Abstract

We bootstrap the symbol of the maximal-helicity-violating four-particle form factor for the chiral part of the stress-tensor supermultiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory at two loops. When minimally normalized, this symbol involves only 34 letters and obeys the extended Steinmann relations in all partially-overlapping three-particle momentum channels. In addition, the remainder function for this form factor exhibits an antipodal self-duality: it is invariant under the combined operation of the antipodal map defined on multiple polylogarithms -- which reverses the order of the symbol letters -- and a simple kinematic map. This self-duality holds on a four-dimensional parity-preserving kinematic hypersurface. It implies the antipodal duality recently noticed between the three-particle form factor and the six-particle amplitude in this theory.

9 pages, 1 figure and 1 table. v2: minor clarifications, references added, journal version. v3: ancillary file containing 3 loop symbol added

References in corpus (97)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Magic identities for conformal four-point integrals
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• 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
• Comments on gluon scattering amplitudes via AdS/CFT
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• From polygons and symbols to polylogarithmic functions
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Bootstrapping the three-loop hexagon
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Motivic Amplitudes and Cluster Coordinates
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• An Operator Product Expansion for Polygonal null Wilson Loops
• 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
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Two-Loop QCD Corrections to the Helicity Amplitudes for $H\to$ 3 partons
• Heptagons from the Steinmann Cluster Bootstrap
• 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
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• 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
• Harmony of Super Form Factors
• Two-Loop Integrals for Planar Five-Point One-Mass Processes
• Scattering Amplitudes and Wilson Loops in Twistor Space
• OPE for all Helicity Amplitudes
• The algebraic structure of cut Feynman integrals and the diagrammatic coaction
• One-loop phi-MHV amplitudes using the unitarity bootstrap
• Cluster adjacency and the four-loop NMHV heptagon
• Cluster algebras for Feynman integrals
• One-loop Higgs plus four gluon amplitudes: Full analytic results
• From multiple unitarity cuts to the coproduct of Feynman integrals
• On the collinear limit of scattering amplitudes at strong coupling
• The Double Pentaladder Integral to All Orders
• A Three-Point Form Factor Through Five Loops
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• Two-Loop Hexa-Box Integrals for Non-Planar Five-Point One-Mass Processes
• Rationalizing Loop Integration
• Cluster adjacency beyond MHV
• 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
• Sequential Discontinuities of Feynman Integrals and the Monodromy Group
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Fermionic pentagons and NMHV hexagon
• How tropical are seven- and eight-particle amplitudes?
• Implications of the Landau Equations for Iterated Integrals
• One-loop phi-MHV amplitudes using the unitarity bootstrap: the general helicity case
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• One-loop helicity amplitudes for H -> gluons: the all-minus configuration
• Folding Amplitudes into Form Factors: An Antipodal Duality
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• Lifting Heptagon Symbols to Functions
• Tropical Grassmannians, cluster algebras and scattering amplitudes
• An Operator Product Expansion for Form Factors
• What is the $i\epsilon$ for the S-matrix?
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• Symbol Alphabets from Plabic Graphs
• Tropical fans, scattering equations and amplitudes
• Notes on cluster algebras and some all-loop Feynman integrals
• On factorization of multiparticle pentagons
• All-Mass $n$-gon Integrals in $n$ Dimensions
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Symbol Alphabets from Tensor Diagrams
• Dual conformal invariance for form factors
• Matrix pentagons
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• Schubert Problems, Positivity and Symbol Letters
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• The Two-Loop Remainder Function for Eight and Nine Particles
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• Symbol Alphabets from Plabic Graphs II: Rational Letters
• One-loop hexagon integral to higher orders in the dimensional regulator
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• Antipodal Symmetry of Two-Loop MHV Amplitudes
• Deciphering the Maximal Transcendentality Principle via Bootstrap

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• Bootstrapping elliptic Feynman integrals using Schubert analysis
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• An Infinite Family of Elliptic Ladder Integrals
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• A Two-Loop Four-Point Form Factor at Function Level
• All Two-Loop Feynman Integrals for Five-Point One-Mass Scattering
• 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