Hexagon POPE: effective particles and tree level resummation

Abstract

We present the resummation of the full Pentagon Operator Product Expansion series of the hexagon Wilson loop in planar $\mathcal{N}=4$ SYM at tree level. We do so by considering the one effective particle states formed by a fundamental flux tube excitation and an arbitrary number of the so called "small fermions" which are then integrated out. We present our proposals for the one effective particle measures at finite coupling. By evaluating these measures at tree level and summing over all one effective particle states we reproduce the full 6 point tree level amplitude.

29 pages, 8 figures

References in corpus (15)

• 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
• Comments on operators with large spin
• An Operator Product Expansion for Polygonal null Wilson Loops
• All tree-level amplitudes in N=4 SYM
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• OPE for all Helicity Amplitudes
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Hexagon OPE Resummation and Multi-Regge Kinematics
• On factorization of multiparticle pentagons
• Strong Wilson polygons from the lodge of free and bound mesons

Cited by in corpus (13)

• Heptagons from the Steinmann Cluster Bootstrap
• Structure constants at wrapping order
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• 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
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• ABJM flux-tube and scattering amplitudes
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• An Operator Product Expansion for Form Factors II. Born level
• Hexagon Bootstrap in the Double Scaling Limit