The hypersimplex canonical forms and the momentum amplituhedron-like logarithmic forms

Tomasz Lukowski, Jonah Stalknecht

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Abstract

In this paper we provide a formula for the canonical differential form of the hypersimplex Δ k,n for all n and k. We also study the generalization of the momentum amplituhedron Mn,k to m = 2, which has been conjectured to share many properties with the hypersimplex, and we provide counterexamples for these conjectures. Nevertheless, we find interesting momentum amplituhedron-like logarithmic differential forms in the m = 2 version of the spinor helicity space, that have the same singularity structure as the hypersimplex canonical forms.

Original languageEnglish
Article number205202
Pages (from-to)1-20
Number of pages20
JournalJournal of Physics A: Mathematical and Theoretical
Volume55
Issue number20
DOIs
Publication statusPublished - 20 Apr 2022

Keywords

  • hep-th
  • math.AG
  • hypersimplex
  • momentum amplituhedron
  • scattering amplitudes
  • positive geometries

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