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Report number	arXiv:1003.1702 ; IPPP-10-21 ; DCPT-10-42 ; CERN-PH-TH-2010-059 ; IPPP-10-21 ; DCPT-10-42 ; CERN-PH-TH-2010-059
Title	The Two-Loop Hexagon Wilson Loop in N = 4 SYM
Author(s)	Del Duca, Vittorio (CERN ; Frascati) ; Duhr, Claude (Durham U., IPPP) ; Smirnov, Vladimir A. (Moscow State U. ; SINP, Moscow)
Publication	2010
Imprint	09 Mar 2010
Number of pages	119
Note	Comments: 120 pages. References added and typos in Appendix G corrected. 120 pages. References added and typos in Appendix G corrected.
In:	JHEP 05 (2010) 084
DOI	10.1007/JHEP05(2010)084
Subject category	Particle Physics - Theory
Abstract	In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetry constrains multi-loop n-edged Wilson loops to be given in terms of the one-loop n-edged Wilson loop, augmented, for n greater than 6, by a function of conformally invariant cross ratios. That function is termed the remainder function. In a recent paper, we have displayed the first analytic computation of the two-loop six-edged Wilson loop, and thus of the corresponding remainder function. Although the calculation was performed in the quasi-multi-Regge kinematics of a pair along the ladder, the Regge exactness of the six-edged Wilson loop in those kinematics entails that the result is the same as in general kinematics. We show in detail how the most difficult of the integrals is computed, which contribute to the six-edged Wilson loop. Finally, the remainder function is given as a function of uniform transcendental weight four in terms of Goncharov polylogarithms. We consider also some asymptotic values of the remainder function, and the value when all the cross ratios are equal.
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