Simplicity of Polygon Wilson Loops in N=4 SYM

Details Simplicity of Polygon Wilson Loops in N=4 SYM Simplicity of Polygon Wilson Loops in N=4 SYM

2009-10-26

arxiv.org/abs/0910.4898v2

JHEP 1001:050,2010

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1007/JHEP01(2010)050

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.

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