University of Hertfordshire

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

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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

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.

Notes

© 2022 The Author(s). Published by IOP Publishing Ltd. This is an open access article distributed under the Creative Commons Attribution License, to view a copy of the license, see: https://creativecommons.org/licenses/by/4.0/

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