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Wilson Loops @ 3-Loops in Special Kinematics · Around

2011

Wilson Loops @ 3-Loops in Special Kinematics

Heslop, Paul, Khoze, Valentin V.

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We obtain a compact expression for the octagon MHV amplitude / Wilson loop at 3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed coefficients.

We do this by making use of the cyclic and parity symmetry of the amplitude/Wilson loop and its behaviour in the soft/collinear limits as well as in the leading term in the expansion away from this limit.
We also make a natural and quite general assumption about the functional form of the result, namely that it should consist of weight 6 polylogarithms whose symbol consists of basic cross-ratios only (and not functions thereof).
We also describe the uplift of this result to 10 points.

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C. Anastasiou, Z. Bern, L. J. Dixon and D. A. Kosower,
2003
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R. Britto, F. Cachazo, B. Feng, E. Witten,
2005
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Z. Bern, L. J. Dixon and V. A. Smirnov,
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L. F. Alday and J. Maldacena,
2007
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J. M. Drummond, G. P. Korchemsky and E. Sokatchev,
2008
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A. Brandhuber, P. Heslop and G. Travaglini,
2008
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J. M. Drummond, J. Henn, G. P. Korchemsky and E. Sokatchev,
2008
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