Hexagon Wilson Loop OPE and Harmonic Polylogarithms

Abstract

A recent, integrability-based conjecture in the framework of the Wilson loop OPE for N=4 SYM theory, predicts the leading OPE contribution for the hexagon MHV remainder function and NMHV ratio function to all loops, in integral form. We prove that these integrals evaluate to a particular basis of harmonic polylogarithms, at any order in the weak coupling expansion. The proof constitutes an algorithm for the direct computation of the integrals, which we employ in order to obtain the full (N)MHV OPE contribution in question up to 6 loops, and certain parts of it up to 12 loops. We attach computer-readable files with our results, as well as an algorithm implementation which may be readily used to generate higher-loop corrections. The feasibility of obtaining the explicit kinematical dependence of the first term in the OPE in principle at arbitrary loop order, offers promise for the suitability of this approach as a non-perturbative description of Wilson loops/scattering amplitudes.

34 pages, 4 figures, 7 ancillary files; v2: typos corrected, references updated

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Cited by in corpus (43)

• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• 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
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• The Double Pentaladder Integral to All Orders
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Nonsinglet pentagons and NMHV amplitudes
• Fermionic pentagons and NMHV hexagon
• How tropical are seven- and eight-particle amplitudes?
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• All-order amplitudes at any multiplicity in the multi-Regge limit
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Evaluating the 6-point Remainder Function Near the Collinear Limit
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• On factorization of multiparticle pentagons
• Wilson loop OPE, analytic continuation and multi-Regge limit
• The Two-Loop Symbol of all Multi-Regge Regions
• Cluster Polylogarithms for Scattering Amplitudes
• Hexagon POPE: effective particles and tree level resummation
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• The four-loop six-gluon NMHV ratio function
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• Strong Wilson polygons from the lodge of free and bound mesons
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• Descent equation for superloop and cyclicity of OPE
• The Multi-Regge Limit from the Wilson Loop OPE
• Hexagon Bootstrap in the Double Scaling Limit
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM