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

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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 N2MHV 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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Authors and Affiliations

  1. Niels Bohr International Academy and Discovery Center, Blegdamsvej 17, Copenhagen, 2100, Denmark

    Simon Caron-Huot

  2. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A

    Simon Caron-Huot & Song He

  3. Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada

    Song He

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  1. Simon Caron-Huot
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  2. Song He
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Correspondence to Song He.

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ArXiv ePrint: 1305.2781

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Caron-Huot, S., He, S. Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory. J. High Energ. Phys. 2013, 101 (2013). https://doi.org/10.1007/JHEP08(2013)101

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