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The momentum amplituhedron

  • David Damgaard
  • Livia Ferro
  • Tomasz LukowskiEmail author
  • Matteo Parisi
Open Access
Regular Article - Theoretical Physics

Abstract

In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in \( \mathcal{N} \) = 4 super Yang-Mills theory in spinor helicity space. Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region. The momentum amplituhedron Mn,k is then the image of the positive Grassmannian via a map determined by such kinematics. The scattering amplitudes are extracted from the canonical form with logarithmic singularities on the boundaries of this geometry.

Keywords

Scattering Amplitudes Supersymmetric Gauge Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • David Damgaard
    • 1
  • Livia Ferro
    • 1
    • 2
  • Tomasz Lukowski
    • 2
    Email author
  • Matteo Parisi
    • 3
  1. 1.Arnold-Sommerfeld-Center for Theoretical PhysicsLudwig-Maximilians-UniversitätMünchenGermany
  2. 2.School of Physics, Astronomy and MathematicsUniversity of HertfordshireHertfordshireU.K.
  3. 3.Mathematical InstituteUniversity of OxfordOxfordU.K.

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