Multichannel Conformal Blocks for Polygon Wilson Loops

Abstract

We introduce the notion of Multichannel Conformal Blocks relevant for the Operator Product Expansion for Null Polygon Wilson loops with more than six edges. As an application of these, we decompose the one loop heptagon Wilson loop and predict the value of its two loop OPE discontinuities. At the functional level, the OPE discontinuities are roughly half of the full result. Using symbols they suffice to predict the full two loop result. We also present several new predictions for the heptagon result at any loop order.

19 pages, 6 figures. v2: typos corrected

References in corpus (21)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• 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
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• An Operator Product Expansion for Polygonal null Wilson Loops
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• Notes on the scattering amplitude / Wilson loop duality
• Pulling the straps of polygons
• Exciting the GKP string at any coupling
• Are scattering amplitudes dual to super Wilson loops?
• Bootstrapping Null Polygon Wilson Loops
• HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables
• HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4
• Analytic Results for MHV Wilson Loops
• A Two-Loop Octagon Wilson Loop in N = 4 SYM
• Holomorphic Linking, Loop Equations and Scattering Amplitudes in Twistor Space
• Tables of the Appell Hypergeometric Functions $F_2$
• Collinear and Regge behavior of 2 -> 4 MHV amplitude in N = 4 super Yang-Mills theory

Cited by in corpus (24)

• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Bootstrapping the three-loop hexagon
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• 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
• Heptagons from the Steinmann Cluster Bootstrap
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Multipoint Conformal Blocks in the Comb Channel
• OPE for all Helicity Amplitudes
• BFKL approach and 2->5 MHV amplitude
• The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
• The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory
• Luescher formula for GKP string
• On factorization of multiparticle pentagons
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• The Two-Loop Symbol of all Multi-Regge Regions
• Defect Conformal Blocks from Appell Functions
• Multichannel conformal blocks for scattering amplitudes
• Resummed tree heptagon
• MHV amplitudes at strong coupling and linearized TBA equations
• ABJM flux-tube and scattering amplitudes
• The Multi-Regge Limit from the Wilson Loop OPE
• Differential equations for multi-loop integrals and two-dimensional kinematics