Two-Loop Polygon Wilson Loops in N=4 SYM

Abstract

We compute for the first time the two-loop corrections to arbitrary n-gon lightlike Wilson loops in N=4 supersymmetric Yang-Mills theory, using efficient numerical methods. The calculation is motivated by the remarkable agreement between the finite part of planar six-point MHV amplitudes and hexagon Wilson loops which has been observed at two loops. At n=6 we confirm that the ABDK/BDS ansatz must be corrected by adding a remainder function, which depends only on conformally invariant ratios of kinematic variables. We numerically compute remainder functions for n=7,8 and verify dual conformal invariance. Furthermore, we study simple and multiple collinear limits of the Wilson loop remainder functions and demonstrate that they have precisely the form required by the collinear factorisation of the corresponding two-loop n-point amplitudes. The number of distinct diagram topologies contributing to the n-gon Wilson loops does not increase with n, and there is a fixed number of "master integrals", which we have computed. Thus we have essentially computed general polygon Wilson loops, and if the correspondence with amplitudes continues to hold, all planar n-point two-loop MHV amplitudes in the N=4 theory.

54 pages, 13 figures. v4: minor typo in the definition of the hard integral corrected v3: references added, minor corrections. v2: typos corrected, one reference added

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• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• On planar gluon amplitudes/Wilson loops duality
• 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
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Universal structure of subleading infrared poles in gauge theory amplitudes
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• All tree-level amplitudes in N=4 SYM
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• QCD corrections to tri-boson production
• Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• The two-loop QCD amplitude gg -> h,H in the Minimal Supersymmetric Standard Model
• Iterated amplitudes in the high-energy limit
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
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Cited by in corpus (85)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Motivic Amplitudes and Cluster Coordinates
• Thermodynamic Bubble Ansatz
• Y-system for Scattering Amplitudes
• Towards a Basis for Planar Two-Loop Integrals
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• 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
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• Form factors at strong coupling via a Y-system
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Hexagon functions and the three-loop remainder function
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Pulling the straps of polygons
• 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
• Exacting N=4 Superconformal Symmetry
• Symmetries and analytic properties of scattering amplitudes in N=4 SYM theory
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• Solution to the Ward Identities for Superamplitudes
• Are scattering amplitudes dual to super Wilson loops?
• The last of the simple remainders
• Bootstrapping Null Polygon Wilson Loops
• MHV Diagrams in Momentum Twistor Space
• More loops and legs in Higgs-regulated N=4 SYM amplitudes
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
• Analytic Results for MHV 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
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• Simplicity of Polygon Wilson Loops in N=4 SYM
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• From Correlators to Wilson Loops in Chern-Simons Matter Theories
• The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
• Correlation function of null polygonal Wilson loops with local operators
• Scattering in ABJ theories
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• The one-loop pentagon to higher orders in epsilon
• Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
• Wilson Loops @ 3-Loops in Special Kinematics
• On wrapping corrections to GKP-like operators
• Light-like Wilson loops in ABJM and maximal transcendentality
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• 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
• Six-point gluon scattering amplitudes from Z_4-symmetric integrable model
• Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture
• The Two-Loop Remainder Function for Eight and Nine Particles
• The Imaginary Part of the N = 4 Super-Yang-Mills Two-Loop Six-Point MHV Amplitude in Multi-Regge Kinematics
• Null Polygonal Wilson Loops in Full N=4 Superspace
• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory
• Cross-Order Integral Relations from Maximal Cuts
• T-functions and multi-gluon scattering amplitudes
• 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
• Hidden Simplicity of Gauge Theory Amplitudes
• 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
• Observations on Open and Closed String Scattering Amplitudes at High Energies
• Conformal anomaly of super Wilson loop
• ABJM amplitudes and WL at finite N
• Some analytic results for two-loop scattering amplitudes
• Wilson loop remainder function for null polygons in the limit of self-crossing
• Series Solution and Minimal Surfaces in AdS
• Scattering amplitudes at strong coupling for 4K gluons
• Uplifting Amplitudes in Special Kinematics
• Aspects of the N=4 SYM amplitude -- Wilson polygon duality
• Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory
• A Note on Dual MHV Diagrams in N=4 SYM
• A Surprise in the Amplitude/Wilson Loop Duality
• Regular Wilson loops and MHV amplitudes at weak and strong coupling
• Cluster algebras in scattering amplitudes with special 2D kinematics
• 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
• A note on two-loop superloop
• Classical gravitational scattering from a gauge-invariant double copy
• Twistors, Harmonics and Holomorphic Chern-Simons