Simplicity of Polygon Wilson Loops in N=4 SYM

Abstract

Wilson loops with lightlike polygonal contours have been conjectured to be equivalent to MHV scattering amplitudes in N=4 super Yang-Mills. We compute such Wilson loops for special polygonal contours at two loops in perturbation theory. Specifically, we concentrate on the remainder function R, obtained by subtracting the known ABDK/BDS ansatz from the Wilson loop. First, we consider a particular two-dimensional eight-point kinematics studied at strong coupling by Alday and Maldacena. We find numerical evidence that R is the same at weak and at strong coupling, up to an overall, coupling-dependent constant. This suggests a universality of the remainder function at strong and weak coupling for generic null polygonal Wilson loops, and therefore for arbitrary MHV amplitudes in N=4 super Yang-Mills. We analyse the consequences of this statement. We further consider regular n-gons, and find that the remainder function is linear in n at large n through numerical computations performed up to n=30. This reproduces a general feature of the corresponding strong-coupling result.

28 pages, 11 figures, pdflatex. v2 minor typos corrected

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• Gluon scattering amplitudes at strong coupling
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• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
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• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
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• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
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• General properties of multiparton webs: proofs from combinatorics
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• A simple collinear limit of scattering amplitudes at strong coupling
• Six-point gluon scattering amplitudes from Z_4-symmetric integrable model
• g-Functions and gluon scattering amplitudes at strong coupling
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• T-functions and multi-gluon scattering amplitudes
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• Series Solution and Minimal Surfaces in AdS
• Scattering amplitudes at strong coupling for 4K gluons
• Cluster algebras in scattering amplitudes with special 2D kinematics
• Regular Wilson loops and MHV amplitudes at weak and strong coupling
• MHV amplitudes at strong coupling and linearized TBA equations
• Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling
• Antenna Operator Product Expansion of ABJ(M) Lightlike Polygon Wilson Loop
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