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Two-loop polygon Wilson loops in Script N = 4 SYM

Anastasiou, Charalampos; Brandhuber, Andreas; Heslop, Paul; Khoze, Valentin V.; Spence, Bill; Travaglini, G.


Charalampos Anastasiou

Andreas Brandhuber

Paul Heslop

Bill Spence

G. Travaglini


We compute for the first time the two-loop corrections to arbitrary n-gon lightlike Wilson loops in Script N = 4 supersymmetric Yang-Mills theory, using efficient numerical methods. The calculation is motivated by the remarkable agreement between the finite part of planar six-point MHV amplitudes and hexagon Wilson loops which has been observed at two loops. At n = 6 we confirm that the ABDK/BDS ansatz must be corrected by adding a remainder function, which depends only on conformally invariant ratios of kinematic variables. We numerically compute remainder functions for n = 7,8 and verify dual conformal invariance. Furthermore, we study simple and multiple collinear limits of the Wilson loop remainder functions and demonstrate that they have precisely the form required by the collinear factorisation of the corresponding two-loop n-point amplitudes. The number of distinct diagram topologies contributing to the n-gon Wilson loops does not increase with n, and there is a fixed number of ``master integrals", which we have computed. Thus we have essentially computed general polygon Wilson loops, and if the correspondence with amplitudes continues to hold, all planar n-point two-loop MHV amplitudes in the Script N = 4 theory.

Journal Article Type Article
Acceptance Date May 7, 2009
Online Publication Date May 27, 2009
Publication Date 2009
Deposit Date Jan 30, 2012
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Electronic ISSN 1029-8479
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2009
Issue 05
Article Number 115
Public URL
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