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The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory · Around

2013

The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory

Golden, John, Spradlin, Marcus

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We present an explicit analytic calculation of the differential of the planar n-particle, two-loop MHV scattering amplitude in N=4 super Yang-Mills theory.

The result is expressed only in terms of the polylogarithm functions Li_k(-x), for k=1,2,3, with arguments x belonging to the special class of dual conformal cross-ratios known as cluster X-coordinates.
The surprising fact that these amplitudes may be expressed in this way provides a striking example of the manner in which the cluster structure on the kinematic configuration space underlies the structure of amplitudes in SYM theory.

Built on

C. Anastasiou, Z. Bern, L. J. Dixon and D. A. Kosower, “Planar amplitudes in maximally supersymmetric Yang-Mills theory,” Phys. Rev. Lett. 91
2003
Earlier work this paper cites.
Z. Bern, L. J. Dixon and V. A. Smirnov, “Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond,” Phys. Rev. D 72
2005
Earlier work this paper cites.
C. Anastasiou, A. Brandhuber, P. Heslop, V. V. Khoze, B. Spence and G. Travaglini, “Two-Loop Polygon Wilson Loops in N = 4 N=4 SYM,” JHEP 0905
Original
2009
Earlier work this paper cites.

Similar

P. Heslop and V. V. Khoze, “Analytic Results for MHV Wilson Loops,” JHEP 1011
Original
2010
Cited alongside, same era.
A. B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, “Classical Polylogarithms for Amplitudes and Wilson Loops,” Phys. Rev. Lett. 105
Original
2010
Cited alongside, same era.
S. Caron-Huot, “Superconformal symmetry and two-loop amplitudes in planar N = 4 N=4 super Yang-Mills,” JHEP 1112
Original
2011
Cited alongside, same era.
J. Golden, A. B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, “Motivic Amplitudes and Cluster Coordinates,” arXiv:1305.1617 [hep-th]
Original
Cited in the paper.
N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. B. Goncharov, A. Postnikov and J. Trnka, “Scattering Amplitudes and the Positive Grassmannian,” arXiv:1212.5605 [hep-th]
Original
Cited in the paper.

Then

D. Gaiotto, J. Maldacena, A. Sever and P. Vieira, “Pulling the straps of polygons,” JHEP 1112
Original
2011
Later among the works it cites.
A. Sever and P. Vieira, JHEP 1201
Original
2012
Later among the works it cites.
A. Hodges, “Eliminating spurious poles from gauge-theoretic amplitudes,” JHEP 1305
Original
2013
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