Regular Wilson loops and MHV amplitudes at weak and strong coupling

Abstract

Traditionally, the duality between Wilson loops and amplitudes beyond one loop in N=4 SYM is characterised by the remainder function. Because of the perturbative origins of the BDS expression, the remainder function is more natural at weak than at strong coupling. We advocate instead a more direct approach, based on considering ratios of Wilson loops. This allows us to define a manifestly finite, regularisation independent, conformally invariant quantity. It does not make a direct reference to the BDS expression and the definition is regularisation independent. It is a natural object at weak and at strong coupling, and in the latter case is directly related to the free energy of an auxiliary integrable system. We then compute these ratios for continuous families of regular polygons for 6,8 and 10 points at one and two-loops. These results are compared to expressions derived recently at strong coupling.

v3 corrected discussion of octagon AdS3 kinematics. v2 extended discussion of multi-collinear limits, new figure, reference added. 23 pages, 6 figures

References in corpus (13)

• 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
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• Scattering into the fifth dimension of N=4 super Yang-Mills
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• Simplicity of Polygon Wilson Loops in N=4 SYM
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• Scattering amplitudes in strongly coupled N=4 SYM from semiclassical strings in AdS

Cited by in corpus (8)

• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• General properties of multiparton webs: proofs from combinatorics
• Analytic Results for MHV Wilson Loops
• A simple collinear limit of scattering amplitudes at strong coupling
• T-functions and multi-gluon scattering amplitudes
• Scattering amplitudes at strong coupling for 4K gluons
• Uplifting Amplitudes in Special Kinematics
• A Surprise in the Amplitude/Wilson Loop Duality