Notes on the scattering amplitude / Wilson loop duality

Abstract

We consider the duality between the four-dimensional S-matrix of planar maximally supersymmetric Yang-Mills theory and the expectation value of polygonal shaped Wilson loops in the same theory. We extend the duality to amplitudes with arbitrary helicity states by introducing a suitable supersymmetric extension of the Wilson loop. We show that this object is determined by a host of recursion relations, which are valid at tree level and at loop level for a certain "loop integrand" defined within the Lagrangian insertion procedure. These recursion relations reproduce the BCFW ones obeyed by tree-level scattering amplitudes, as well as their extension to loop integrands which appeared recently in the literature, establishing the duality to all orders in perturbation theory. Finally, we propose that a certain set of finite correlation functions can be used to compute all first derivatives of the logarithm of MHV amplitudes.

25 pages + appendix, 5 figures

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• Gluon scattering amplitudes at strong coupling
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• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Magic identities for conformal four-point integrals
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• Hexagon Wilson loop = six-gluon MHV amplitude
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Cited by in corpus (122)

• 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
• 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
• Pulling the straps of polygons
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• Evidence for a Nonplanar Amplituhedron
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• More on the duality correlators/amplitudes
• Prescriptive Unitarity
• OPE for all Helicity Amplitudes
• A Note on Polytopes for Scattering Amplitudes
• Cluster adjacency and the four-loop NMHV heptagon
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• Massive amplitudes on the Coulomb branch of N=4 SYM
• Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
• On MHV Form Factors in Superspace for $\mathcal{N}=4$ SYM Theory
• Ten dimensional symmetry of N=4 SYM correlators
• Conformal Anomaly for Amplitudes in N=6 Superconformal Chern-Simons Theory
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Nonsinglet pentagons and NMHV amplitudes
• Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
• Exact Bremsstrahlung and Effective Couplings
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Yangian Symmetry of smooth Wilson Loops in N=4 super Yang-Mills Theory
• Fermionic pentagons and NMHV hexagon
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• One Loop Amplitudes In ABJM
• The Exact Effective Couplings of 4D N=2 gauge theories
• Gravity On-shell Diagrams
• The Amplituhedron from Momentum Twistor Diagrams
• An Introduction to On-shell Recursion Relations
• On NMHV form factors in N=4 SYM theory from generalized unitarity
• Star Integrals, Convolutions and Simplices
• Quantum mechanics of null polygonal Wilson loops
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• Nonperturbative Negative Geometries: Amplitudes at Strong Coupling and the Amplituhedron
• 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
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• Notes on cluster algebras and some all-loop Feynman integrals
• On factorization of multiparticle pentagons
• Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes
• Amplitudes of 3d Yang Mills Theory
• Correlation functions, null polygonal Wilson loops, and local operators
• From Polygon Wilson Loops to Spin Chains and Back
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Wilson Loops @ 3-Loops in Special Kinematics
• Multichannel Conformal Blocks for Polygon Wilson Loops
• Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory
• OPE for Super Loops
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• OPE for null Wilson loops and open spin chains
• Colour-Twist Operators I: Spectrum and Wave Functions
• The Wilson-loop $d\log$ representation for Feynman integrals
• Integrability of Smooth Wilson Loops in N=4 Superspace
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Null Polygonal Wilson Loops in Full N=4 Superspace
• MHV Diagrams from an All-Line Recursion Relation
• Lightlike contours with fermions
• Amplituhedra, and Beyond
• Scattering Amplitudes and Toric Geometry
• Smooth Wilson Loops in N=4 Non-Chiral Superspace
• Conformal anomaly of super Wilson loop
• On the amplitudes in N=(1,1) D=6 SYM
• One-Loop Soft Theorems via Dual Superconformal Symmetry
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• Dual conformal symmetry on the light-cone
• 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
• Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
• On the Geometry of Null Polygons in Full N=4 Superspace
• Non-planar BCFW Grassmannian Geometries
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Uplifting Amplitudes in Special Kinematics
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• Notes on conformal integrals: Coulomb branch amplitudes, magic identities and bootstrap
• WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Simplifying instanton corrections to N=4 SYM correlators
• 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
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• Supersymmetric Wilson Loops via Integral Forms
• A note on two-loop superloop
• Superpropagator and superconformal invariants
• Scattering Amplitudes of Massive N=2 Gauge Theories in Three Dimensions
• Wilson loops in N=6 superspace for ABJM theory
• Vertex Operators of Super Wilson Loops
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• ABJM flux-tube and scattering amplitudes
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Yangian symmetry of light-like Wilson loops
• Twistors, Harmonics and Holomorphic Chern-Simons
• Gravitation in terms of observables
• Yangian Symmetry in Five Dimensions
• $\mathcal{N}=3$ Harmonic Super-Wilson Loop
• Gravitation in terms of observables 2: the algebra of fundamental observables
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• On Solving Dual Conformal Integrals in Coulomb-branch Amplitudes and Their Periods
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons
• Dilogarithm ladders from Wilson loops