The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space

Abstract

We propose that the complete planar S-matrix of N=4 super Yang-Mills - including all N^kMHV partial amplitudes to all loops - is equivalent to the correlation function of a supersymmetric Wilson loop in twistor space. Remarkably, the entire classical S-matrix arises from evaluating the correlation function in the self-dual sector, while the expansion of the correlation function in powers of the Yang-Mills coupling constant provides the loop expansion of the amplitudes. We support our proposal with explicit computations of the n particle NMHV and NNMHV trees, the integrands of the 1-loop MHV and NMHV amplitudes, and the n particle 2-loop MHV amplitude. These calculations are performed using the twistor action in axial gauge. In this gauge, the Feynman diagrams of the correlation function are the planar duals of the usual MHV diagrams for the scattering amplitude. The results are presented in the form of a sum of products of dual superconformal invariants in (momentum) twistor space, and agree with the expressions derived in arXiv:1009.1854 directly from the MHV rules. The twistor space Wilson loop is a natural supersymmetric generalization of the standard Wilson loop used to compute MHV amplitudes. We show how the Penrose-Ward transform can be used to determine a corresponding supersymmetrization on space-time.

36 pages, 10 figures. Substantial clarification added to section 6

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Cited by in corpus (186)

• The Amplituhedron
• Local Integrals for Planar Scattering Amplitudes
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Bootstrapping an NMHV amplitude through three loops
• Uniqueness of two-loop master contours
• 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
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• The super-correlator/super-amplitude duality: Part I
• Pulling the straps of polygons
• Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Scattering Amplitudes
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Harmony of Super Form Factors
• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• Evidence for a Nonplanar Amplituhedron
• Tree-level Amplitudes in the Nonlinear Sigma Model
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• New differential equations for on-shell loop integrals
• Generic multiloop methods and application to N=4 super-Yang-Mills
• More on the duality correlators/amplitudes
• Prescriptive Unitarity
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Scattering amplitudes: the most perfect microscopic structures in the universe
• OPE for all Helicity Amplitudes
• A Note on Polytopes for Scattering Amplitudes
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Cluster adjacency and the four-loop NMHV heptagon
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• The super-correlator/super-amplitude duality: Part II
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• Massive amplitudes on the Coulomb branch of N=4 SYM
• Are scattering amplitudes dual to super Wilson loops?
• Bootstrapping Null Polygon Wilson Loops
• MHV Diagrams in Momentum Twistor Space
• Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
• Ten dimensional symmetry of N=4 SYM correlators
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• Nonsinglet pentagons and NMHV amplitudes
• Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
• Twistor theory at fifty: from contour integrals to twistor strings
• Conformal and Einstein gravity from twistor actions
• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• Fermionic pentagons and NMHV hexagon
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• One Loop Amplitudes In ABJM
• Gravity On-shell Diagrams
• On NMHV form factors in N=4 SYM theory from generalized unitarity
• The Amplituhedron from Momentum Twistor Diagrams
• An Introduction to On-shell Recursion Relations
• The Correlahedron
• Star Integrals, Convolutions and Simplices
• Quantum mechanics of null polygonal Wilson loops
• MHV diagrams in twistor space and the twistor action
• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• New structures in scattering amplitudes: a review
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Dual Conformal Structure Beyond the Planar Limit
• Tree-Level Formalism
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• Descent equations for superamplitudes
• Notes on cluster algebras and some all-loop Feynman integrals
• Holomorphic Linking, Loop Equations and Scattering Amplitudes in Twistor Space
• Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory
• Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes
• On factorization of multiparticle pentagons
• Traintrack Calabi-Yaus from Twistor Geometry
• Maximal Unitarity for the Four-Mass Double Box
• When does the gluon reggeize?
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• Amplitudes of 3d Yang Mills Theory
• Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
• From Polygon Wilson Loops to Spin Chains and Back
• Correlation functions, null polygonal Wilson loops, and local operators
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• Multichannel Conformal Blocks for Polygon Wilson Loops
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Wilson Loops @ 3-Loops in Special Kinematics
• Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory
• Higher-spin Yang-Mills, amplitudes and self-duality
• OPE for Super Loops
• On Form Factors and Correlation Functions in Twistor Space
• Gluon scattering on self-dual radiative gauge fields
• Bootstrapping six-gluon scattering in planar $\mathcal{N}=4$ super-Yang-Mills theory
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• OPE for null Wilson loops and open spin chains
• The Wilson-loop $d\log$ representation for Feynman integrals
• Twistor actions for gauge theory and gravity
• Composite operators and form factors in N=4 SYM
• The 4d/2d correspondence in twistor space and holomorphic Wilson lines
• Integrability of Smooth Wilson Loops in N=4 Superspace
• Two-Loop Five-Point Two-Mass Planar Integrals and Double Lagrangian Insertions in a Wilson Loop
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• MHV Diagrams from an All-Line Recursion Relation
• Cross-Order Integral Relations from Maximal Cuts
• Null Polygonal Wilson Loops in Full N=4 Superspace
• Scattering Amplitudes and Toric Geometry
• Hidden Simplicity of Gauge Theory Amplitudes
• Lightlike contours with fermions
• A Gluing Operator for the Ambitwistor String
• Smooth Wilson Loops in N=4 Non-Chiral Superspace
• Integrands for QCD rational terms and N=4 SYM from massive CSW rules
• Conformal anomaly of super Wilson loop
• Demystifying the twistor construction of composite operators in N=4 super-Yang-Mills theory
• The Coulomb-branch S-matrix from massless amplitudes
• The two-loop six-point amplitude in ABJM theory
• Nonperturbative enhancement of superloop at strong coupling
• One-Loop Soft Theorems via Dual Superconformal Symmetry
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Towards NMHV amplitudes at strong coupling
• Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
• Minitwistors and 3d Yang-Mills-Higgs theory
• Dual conformal symmetry on the light-cone
• Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
• On the Geometry of Null Polygons in Full N=4 Superspace
• Correlation functions of the chiral stress-tensor multiplet in N=4 SYM
• Multi-Particle Amplitudes from the Four-Point Correlator in Planar N=4 SYM
• All two-loop MHV remainder functions in multi-Regge kinematics
• On the scattering of gluons in the GKP string
• Twistor fishnets
• Multichannel conformal blocks for scattering amplitudes
• The four-loop six-gluon NMHV ratio function
• Weak Coupling, Degeneration and Log Calabi-Yau Spaces
• Uplifting Amplitudes in Special Kinematics
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• A Note on Dual MHV Diagrams in N=4 SYM
• Recursion and worldsheet formulae for 6d superamplitudes
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• WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory
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• Notes on conformal integrals: Coulomb branch amplitudes, magic identities and bootstrap
• Wilson Loop diagrams and Positroids
• Yangian Symmetry in N=4 super Yang-Mills
• Resummed tree heptagon
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Simplifying instanton corrections to N=4 SYM correlators
• On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• Super Cartan geometry and the super Ashtekar connection
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• Anatomy of the Amplituhedron
• Polylogarithm identities, cluster algebras and the N=4 supersymmetric theory
• A note on two-loop superloop
• Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
• Supersymmetric Wilson Loops via Integral Forms
• Super fiber bundles, connection forms, and parallel transport
• Supersymmetric quantum mechanics of the flux tube
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• Wilson loops in N=6 superspace for ABJM theory
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions
• Superpropagator and superconformal invariants
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• Wilson Loop Form Factors: A New Duality
• Vertex Operators of Super Wilson Loops
• Twistor action for general relativity
• Ambitwistor strings and reggeon amplitudes in N=4 SYM
• Descent equation for superloop and cyclicity of OPE
• Twistors, Harmonics and Holomorphic Chern-Simons
• Lagrangian Insertion in the Light-Like Limit and the Super-Correlators/Super-Amplitudes Duality
• Yangian symmetry of light-like Wilson loops
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Super Wilson Loops and Holonomy on Supermanifolds
• Lectures on twistor theory
• Yangian Symmetry in Five Dimensions
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• A Celestial Description of Planar Super-Yang-Mills Theory
• $\mathcal{N}=3$ Harmonic Super-Wilson Loop
• On Solving Dual Conformal Integrals in Coulomb-branch Amplitudes and Their Periods
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Twistor Parametrization of Locally BPS Super-Wilson Loops
• The Twofold Way of Super Holonomy
• Dilogarithm ladders from Wilson loops
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons