Wilson Loops @ 3-Loops in Special Kinematics

Abstract

We obtain a compact expression for the octagon MHV amplitude / Wilson loop at 3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed coefficients. We do this by making use of the cyclic and parity symmetry of the amplitude/Wilson loop and its behaviour in the soft/collinear limits as well as in the leading term in the expansion away from this limit. We also make a natural and quite general assumption about the functional form of the result, namely that it should consist of weight 6 polylogarithms whose symbol consists of basic cross-ratios only (and not functions thereof). We also describe the uplift of this result to 10 points.

26 pages. Typos corrected

References in corpus (12)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Hexagon Wilson loop = six-gluon MHV amplitude
• Bootstrapping the three-loop hexagon
• 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
• Notes on the scattering amplitude / Wilson loop duality
• On BCFW shifts of integrands and integrals
• Analytic Results for MHV Wilson Loops
• OPE for Super Loops

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• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• Analytic two-loop form factors in N=4 SYM
• The last of the simple remainders
• Mellin Amplitudes for Dual Conformal Integrals
• Star Integrals, Convolutions and Simplices
• Generalised ladders and single-valued polylogarithms
• Superstring amplitudes and the associator
• From Polygon Wilson Loops to Spin Chains and Back
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
• Uplifting Amplitudes in Special Kinematics
• Differential equations for multi-loop integrals and two-dimensional kinematics