An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM

Abstract

In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetry constrains multi-loop n-edged Wilson loops to be basically given in terms of the one-loop n-edged Wilson loop, augmented, for n greater than 6, by a function of conformally invariant cross ratios. We identify a class of kinematics for which the Wilson loop exhibits exact Regge factorisation and which leave invariant the analytic form of the multi-loop n-edged Wilson loop. In those kinematics, the analytic result for the Wilson loop is the same as in general kinematics, although the computation is remarkably simplified with respect to general kinematics. Using the simplest of those kinematics, we have performed the first analytic computation of the two-loop six-edged Wilson loop in general kinematics.

17 pages. Extended discussion on how the QMRK limit is taken. Version accepted by JHEP. A text file containing the Mathematica code with the analytic expression for the 6-point remainder function is included

References in corpus (20)

• 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
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Thermodynamic Bubble Ansatz
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• FIESTA 2: parallelizeable multiloop numerical calculations
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Iterated amplitudes in the high-energy limit
• Simplicity of Polygon Wilson Loops in N=4 SYM
• The Imaginary Part of the N = 4 Super-Yang-Mills Two-Loop Six-Point MHV Amplitude in Multi-Regge Kinematics
• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory

Cited by in corpus (121)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• From polygons and symbols to polylogarithmic functions
• Bootstrapping the three-loop hexagon
• PolyLogTools - Polylogs for the masses
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Motivic Amplitudes and Cluster Coordinates
• Thermodynamic Bubble Ansatz
• Y-system for Scattering Amplitudes
• Towards a Basis for Planar Two-Loop Integrals
• 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
• Bootstrapping an NMHV amplitude through three loops
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Hexagon functions and the three-loop remainder function
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• FIESTA 2: parallelizeable multiloop numerical calculations
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Single-valued harmonic polylogarithms and the multi-Regge limit
• Pulling the straps of polygons
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Elliptic Feynman integrals and pure functions
• On soft singularities at three loops and beyond
• Cluster adjacency properties of scattering amplitudes
• Bootstrapping the QCD soft anomalous dimension
• Scattering Amplitudes
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• The infrared structure of gauge theory amplitudes in the high-energy limit
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• On form factors in N=4 sym
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Are scattering amplitudes dual to super Wilson loops?
• More loops and legs in Higgs-regulated N=4 SYM amplitudes
• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
• Cluster adjacency beyond MHV
• General properties of multiparton webs: proofs from combinatorics
• Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy
• All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes
• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• BFKL approach and 2->5 MHV amplitude
• How tropical are seven- and eight-particle amplitudes?
• Analytic Results for MHV Wilson Loops
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• A Two-Loop Octagon Wilson Loop in N = 4 SYM
• Star Integrals, Convolutions and Simplices
• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• Mandelstam cuts and light-like Wilson loops in N=4 SUSY
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• On convergent series representations of Mellin-Barnes integrals
• The massless hexagon integral in D = 6 dimensions
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• MHV amplitude for 3->3 gluon scattering in Regge limit
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• All-order amplitudes at any multiplicity in the multi-Regge limit
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• The one-loop six-dimensional hexagon integral with three massive corners
• The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• Wilson loop OPE, analytic continuation and multi-Regge limit
• The six-point remainder function to all loop orders in the multi-Regge limit
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Wilson Loops @ 3-Loops in Special Kinematics
• Multi-Regge Limit of the n-Gluon Bubble Ansatz
• Multichannel Conformal Blocks for Polygon Wilson Loops
• OPE for Super Loops
• Analytic properties of high energy production amplitudes in N=4 SUSY
• The One-Loop One-Mass Hexagon Integral in D=6 Dimensions
• OPE for null Wilson loops and open spin chains
• Integrable spin chains and scattering amplitudes
• Six-point gluon scattering amplitudes from Z_4-symmetric integrable model
• The Two-Loop Remainder Function for Eight and Nine Particles
• Solution to Bethe-Salpeter equation via Mellin-Barnes transform
• T-functions and multi-gluon scattering amplitudes
• Cross-Order Integral Relations from Maximal Cuts
• Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
• Symbols of One-Loop Integrals From Mixed Tate Motives
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Cluster Polylogarithms for Scattering Amplitudes
• New four-dimensional integrals by Mellin-Barnes transform
• Null-polygonal minimal surfaces in AdS_4 from perturbed W minimal models
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution
• Conformal anomaly of super Wilson loop
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• Nonperturbative enhancement of superloop at strong coupling
• Some analytic results for two-loop scattering amplitudes
• Multiple polylogarithms in weight 4
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
• All two-loop MHV remainder functions in multi-Regge kinematics
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Uplifting Amplitudes in Special Kinematics
• The four-loop six-gluon NMHV ratio function
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory
• 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
• Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions
• MHV amplitudes at strong coupling and linearized TBA equations
• Impact factors for Reggeon-gluon transition in N = 4 SYM with large number of colours
• One-Loop N = 4 Super Yang-Mills Scattering Amplitudes to All Orders in the Dimensional Regularization Parameter
• A note on two-loop superloop
• Illustrations of Integrand-Basis Building at Two Loops
• The two-loop Higgs impact factor
• One-loop impact factor for the emission of two gluons
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• The long road from Regge poles to the LHC
• Differential equations for multi-loop integrals and two-dimensional kinematics
• Infrared Finite Observables in N=8 Supergravity
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• A tale of two Regge limits
• Discontinuites of BFKL amplitudes and the BDS ansatz
• Hexagon Bootstrap in the Double Scaling Limit
• One-loop central-emission vertex for two gluons in $\mathcal{N}=4$ super Yang-Mills theory
• Progress on the infrared structure of multi-particle gauge theory amplitudes