The Momentum Amplituhedron

David Damgaard, Livia Ferro, Tomasz Lukowski, Matteo Parisi

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)
48 Downloads (Pure)


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 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 M n,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.

Original languageEnglish
Article number42
JournalJournal of High Energy Physics (JHEP)
Issue number8
Publication statusPublished - 8 Aug 2019


  • Scattering Amplitudes
  • Supersymmetric Gauge Theory


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