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 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. That function is termed the remainder function. In a recent paper, we have displayed the first analytic computation of the two-loop six-edged Wilson loop, and thus of the corresponding remainder function. Although the calculation was performed in the quasi-multi-Regge kinematics of a pair along the ladder, the Regge exactness of the six-edged Wilson loop in those kinematics entails that the result is the same as in general kinematics. We show in detail how the most difficult of the integrals is computed, which contribute to the six-edged Wilson loop. Finally, the remainder function is given as a function of uniform transcendental weight four in terms of Goncharov polylogarithms. We consider also some asymptotic values of the remainder function, and the value when all the cross ratios are equal.

120 pages. References added and typos in Appendix G corrected.

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• Hexagon Wilson loop = six-gluon MHV amplitude
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• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• FIESTA 2: parallelizeable multiloop numerical calculations
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• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Analytic two-loop form factors in N=4 SYM
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• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
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• 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
• Hexagon OPE Resummation and Multi-Regge Kinematics
• 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
• Manifestly Dual-Conformal Loop Integration
• On factorization of multiparticle pentagons
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• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
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• Some analytic results for two-loop scattering amplitudes
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