# Two-Loop Polygon Wilson Loops in N=4 SYM - High Energy Physics - Theory

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Abstract: We compute for the first time the two-loop corrections to arbitrary n-gonlightlike Wilson loops in N=4 supersymmetric Yang-Mills theory, using efficientnumerical methods. The calculation is motivated by the remarkable agreementbetween the finite part of planar six-point MHV amplitudes and hexagon Wilsonloops which has been observed at two loops. At n=6 we confirm that the ABDK-BDSansatz must be corrected by adding a remainder function, which depends only onconformally invariant ratios of kinematic variables. We numerically computeremainder functions for n=7,8 and verify dual conformal invariance.Furthermore, we study simple and multiple collinear limits of the Wilson loopremainder functions and demonstrate that they have precisely the form requiredby the collinear factorisation of the corresponding two-loop n-pointamplitudes. The number of distinct diagram topologies contributing to the n-gonWilson loops does not increase with n, and there is a fixed number of -masterintegrals-, which we have computed. Thus we have essentially computed generalpolygon Wilson loops, and if the correspondence with amplitudes continues tohold, all planar n-point two-loop MHV amplitudes in the N=4 theory.

Author: ** Charalampos Anastasiou, Andreas Brandhuber, Paul Heslop, Valentin V. Khoze, Bill Spence, Gabriele Travaglini**

Source: https://arxiv.org/