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 $\Delta_{k,n}$ for all $n$ and $k$. We also study the generalization of the momentum amplituhedron $\mathcal{M}_{n,k}$ to $m=2$, and we conclude that the existing definition does not possess the desired properties. 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
Number of pages24
JournalJournal of Physics A: Mathematical and Theoretical
Early online date30 Mar 2022
DOIs
Publication statusE-pub ahead of print - 30 Mar 2022

Keywords

  • hep-th
  • math.AG

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