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

  • Simon Caron-Huot
  • Song He
Article

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.

Keywords

Scattering Amplitudes Wilson ’t Hooft and Polyakov loops AdS-CFT Correspondence 

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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Niels Bohr International Academy and Discovery CenterCopenhagenDenmark
  2. 2.School of Natural Sciences, Institute for Advanced StudyPrincetonU.S.A
  3. 3.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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