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arXiv · 1305.2781

Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory

Simon Caron-Huot·Song He
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Abstract

We study the S-matrix of planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics; in particular, the higher-point amplitudes we consider can be obtained from those with lowest-points by a collinear uplifting. Based on a compact formula for one-loop N${}^2$MHV amplitudes, we use an equation proposed previously to compute, for the first time, the complete two-loop NMHV and three-loop MHV octagons, which we conjecture to uplift to give the full $n$-point amplitudes up to simpler logarithmic terms or dilogarithmic terms.

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Simon Caron-Huot, Song He. 2013-05-31. Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory. https://doi.org/10.1007/jhep08(2013)101

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