Hexagon Wilson loop = six-gluon MHV amplitude

Abstract

We compare the two-loop corrections to the finite part of the light-like hexagon Wilson loop with the recent numerical results for the finite part of the MHV six-gluon amplitude in N=4 SYM theory by Bern, Dixon, Kosower, Roiban, Spradlin, Vergu and Volovich (arXiv:0803.1465 [hep-th]) and demonstrate that they coincide within the error bars and, at the same time, they differ from the BDS ansatz by a non-trivial function of (dual) conformal kinematical invariants. This provides strong evidence that the Wilson loop/scattering amplitude duality holds in planar N=4 SYM theory to all loops for an arbitrary number of external particles.

34 pages, 3 figures; v2: appendix added, minor corrections made, new references inserted

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• Loop dynamics and AdS/CFT correspondence
• On collinear factorization of Wilson loops and MHV amplitudes in N=4 SYM
• Testing high-energy factorization beyond the next-to-leading-logarithmic accuracy
• Quark scattering amplitudes at strong coupling
• Gluon Scattering in Deformed N=4 SYM

Cited by in corpus (268)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• What is the Simplest Quantum Field Theory?
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• A Duality For The S Matrix
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Bootstrapping the three-loop hexagon
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Motivic Amplitudes and Cluster Coordinates
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Thermodynamic Bubble Ansatz
• Y-system for Scattering Amplitudes
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Scattering into the fifth dimension of N=4 super Yang-Mills
• 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
• Uniqueness of two-loop master contours
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Notes on the scattering amplitude / Wilson loop duality
• Heptagons from the Steinmann Cluster Bootstrap
• 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
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• From correlation functions to Wilson loops
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• The super-correlator/super-amplitude duality: Part I
• From correlation functions to scattering amplitudes
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Leading singularities and off-shell conformal integrals
• Single-valued harmonic polylogarithms and the multi-Regge limit
• 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
• Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• Generalized unitarity for N=4 super-amplitudes
• Exacting N=4 Superconformal Symmetry
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• Webs in multiparton scattering using the replica trick
• 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
• Two-Loop Polygon Wilson Loops in N=4 SYM
• Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
• The Yangian origin of the Grassmannian integral
• Yangians, Grassmannians and T-duality
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
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• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• On form factors in N=4 sym
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• Generic multiloop methods and application to N=4 super-Yang-Mills
• More on the duality correlators/amplitudes
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Scattering Amplitudes and Wilson Loops in Twistor Space
• OPE for all Helicity Amplitudes
• Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
• Cluster adjacency and the four-loop NMHV heptagon
• The super-correlator/super-amplitude duality: Part II
• Solution to the Ward Identities for Superamplitudes
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• Integrability of scattering amplitudes in N=4 SUSY
• Scattering Amplitudes and BCFW Recursion in Twistor Space
• The last of the simple remainders
• Are scattering amplitudes dual to super Wilson loops?
• MHV Diagrams in Momentum Twistor Space
• More loops and legs in Higgs-regulated N=4 SYM amplitudes
• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
• On the collinear limit of scattering amplitudes at strong coupling
• Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
• Local Spacetime Physics from the Grassmannian
• A Three-Point Form Factor Through Five Loops
• Rationalizing Loop Integration
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• Cluster adjacency beyond MHV
• General properties of multiparton webs: proofs from combinatorics
• Ten dimensional symmetry of N=4 SYM correlators
• Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
• Simple loop integrals and amplitudes in N=4 SYM
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• Iterated amplitudes in the high-energy limit
• BFKL approach and 2->5 MHV amplitude
• Supersymmetric Wilson loops at two loops
• Analytic Results for MHV Wilson Loops
• On super form factors of half-BPS operators in N=4 super Yang-Mills
• The Amplituhedron from Momentum Twistor Diagrams
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• A Two-Loop Octagon Wilson Loop in N = 4 SYM
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• Lifting Heptagon Symbols to Functions
• On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• Star Integrals, Convolutions and Simplices
• Mandelstam cuts and light-like Wilson loops in N=4 SUSY
• Implications of multi-Regge limits for the Bern-Dixon-Smirnov conjecture
• Unraveling L_{n,k}: Grassmannian Kinematics
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• The colour octet representation of the non-forward BFKL Green function
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• Duality between Wilson loops and gluon amplitudes
• All-order amplitudes at any multiplicity in the multi-Regge limit
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Analyticity for Multi-Regge Limits of the Bern-Dixon-Smirnov Amplitudes
• Simplicity of Polygon Wilson Loops in N=4 SYM
• From Correlators to Wilson Loops in Chern-Simons Matter Theories
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• Correlation function of null polygonal Wilson loops with local operators
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Dual Conformal Structure Beyond the Planar Limit
• The one-loop six-dimensional hexagon integral with three massive corners
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• Scattering in ABJ theories
• Antipodal Self-Duality for a Four-Particle Form Factor
• Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling
• The one-loop pentagon to higher orders in epsilon
• The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Glueball Dark Matter revisited
• Gluon Reggeization in Yang-Mills Theories
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• Wilson loop OPE, analytic continuation and multi-Regge limit
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Traintrack Calabi-Yaus from Twistor Geometry
• When does the gluon reggeize?
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• The six-point remainder function to all loop orders in the multi-Regge limit
• Correlation functions, null polygonal Wilson loops, and local operators
• From Polygon Wilson Loops to Spin Chains and Back
• Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
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• Analytic result for the one-loop scalar pentagon integral with massless propagators
• Testing high-energy factorization beyond the next-to-leading-logarithmic accuracy
• Wilson Loops @ 3-Loops in Special Kinematics
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Multichannel Conformal Blocks for Polygon Wilson Loops
• Relating amplitude and PDF factorisation through Wilson-line geometries
• OPE for Super Loops
• The One-Loop One-Mass Hexagon Integral in D=6 Dimensions
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• Bootstrapping six-gluon scattering in planar $\mathcal{N}=4$ super-Yang-Mills theory
• Integrable spin chains and scattering amplitudes
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• A simple collinear limit of scattering amplitudes at strong coupling
• OPE for null Wilson loops and open spin chains
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• Six-point gluon scattering amplitudes from Z_4-symmetric integrable model
• Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture
• Twistor actions for gauge theory and gravity
• A Requiem for $Ad{S}_4\times \mathbb{C}{P}^3$ Fermionic self-T-duality
• The Two-Loop Remainder Function for Eight and Nine Particles
• g-Functions and gluon scattering amplitudes at strong coupling
• The Imaginary Part of the N = 4 Super-Yang-Mills Two-Loop Six-Point MHV Amplitude in Multi-Regge Kinematics
• T-functions and multi-gluon scattering amplitudes
• Fermionic T-duality: A snapshot review
• Cross-Order Integral Relations from Maximal Cuts
• IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM Theory
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
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• Smooth Wilson Loops in N=4 Non-Chiral Superspace
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• Null-polygonal minimal surfaces in AdS_4 from perturbed W minimal models
• On the two-loop hexagon Wilson loop remainder function in N=4 SYM
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• Anomalous Dimensions from Soft Regge Constants
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
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• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• A Numerical Study of Gluon Scattering Amplitudes in N=4 Super Yang-Mills Theory at Strong Coupling
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Series Solution and Minimal Surfaces in AdS
• Tree-level amplitudes and dual superconformal symmetry
• On the Classification of Residues of the Grassmannian
• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• Form factors with two operator insertions and the principle of maximal transcendentality
• MHV amplitudes in N=2 SQCD and in N=4 SYM at one loop
• All two-loop MHV remainder functions in multi-Regge kinematics
• The two-loop eight-point amplitude in ABJM theory
• Four-point amplitudes in $\mathcal{N}=2$ SCQCD
• On the Geometry of Null Polygons in Full N=4 Superspace
• Scattering amplitudes at strong coupling for 4K gluons
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory
• Infrared Safe Observables in $\mathcal{N}=4$ Super Yang-Mills Theory
• Uplifting Amplitudes in Special Kinematics
• Aspects of the N=4 SYM amplitude -- Wilson polygon duality
• Hexagon remainder function in the limit of self-crossing up to three loops
• BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time
• The four-loop six-gluon NMHV ratio function
• Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory
• A Surprise in the Amplitude/Wilson Loop Duality
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• Discretized Minimal Surface and the BDS Conjecture in N=4 Super Yang-Mills Theory at Strong Coupling
• A Note on Dual MHV Diagrams in N=4 SYM
• Notes on conformal integrals: Coulomb branch amplitudes, magic identities and bootstrap
• "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• Cluster algebras in scattering amplitudes with special 2D kinematics
• Regular Wilson loops and MHV amplitudes at weak and strong coupling
• An Origin Story for Amplitudes
• Yangian Symmetry in N=4 super Yang-Mills
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Deviation from Alday-Maldacena Duality For Wavy Circle
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• All orders results for self-crossing Wilson loops mimicking double parton scattering
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop
• MHV amplitudes at strong coupling and linearized TBA equations
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• Polylogarithm identities, cluster algebras and the N=4 supersymmetric theory
• One-Loop N = 4 Super Yang-Mills Scattering Amplitudes to All Orders in the Dimensional Regularization Parameter
• Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
• A note on two-loop superloop
• A Two-Loop Four-Point Form Factor at Function Level
• Wilson loops in N=6 superspace for ABJM theory
• The Curious Case of Leading Transcendentality: Three Point Form Factors
• Superpropagator and superconformal invariants
• ABJM flux-tube and scattering amplitudes
• Impact Factors for Reggeon-Gluon Transitions
• The long road from Regge poles to the LHC
• Twistors, strings and supersymmetric gauge theories
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Differential equations for multi-loop integrals and two-dimensional kinematics
• A Note on Loop Amplitudes in QED
• Yangian symmetry of light-like Wilson loops
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Conformal geometry of null hexagons for Wilson loops and scattering amplitudes
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Asymptotic AdS String Solutions for Null Polygonal Wilson Loops in R^{1,2}
• The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory
• MHV amplitudes, Wilson loops and the BDS ansatz in the superconformal N=2 QCD
• Jet Physics from Static Charges in AdS
• Discontinuites of BFKL amplitudes and the BDS ansatz
• $\mathcal{N}=3$ Harmonic Super-Wilson Loop
• A tale of two Regge limits
• Wilson Loops and Integrability
• Dual Conformal Symmetry and Iterative Integrals in Six Dimensions
• On Solving Dual Conformal Integrals in Coulomb-branch Amplitudes and Their Periods
• Theoretical Developments in SUSY
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons
• Duality between Wilson Loops and Scattering Amplitudes
• Gluon scattering amplitudes from gauge/string duality and integrability
• Twistor Parametrization of Locally BPS Super-Wilson Loops
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