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Abstract: In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetryconstrains multi-loop n-edged Wilson loops to be given in terms of the one-loopn-edged Wilson loop, augmented, for n greater than 6, by a function ofconformally invariant cross ratios. That function is termed the remainderfunction. In a recent paper, we have displayed the first analytic computationof the two-loop six-edged Wilson loop, and thus of the corresponding remainderfunction. Although the calculation was performed in the quasi-multi-Reggekinematics of a pair along the ladder, the Regge exactness of the six-edgedWilson loop in those kinematics entails that the result is the same as ingeneral kinematics. We show in detail how the most difficult of the integralsis computed, which contribute to the six-edged Wilson loop. Finally, theremainder function is given as a function of uniform transcendental weight fourin terms of Goncharov polylogarithms. We consider also some asymptotic valuesof the remainder function, and the value when all the cross ratios are equal.



Autor: Vittorio Del Duca, Claude Duhr, Vladimir A. Smirnov

Fuente: https://arxiv.org/



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