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

Tomasz Lukowski; Jonah Stalknecht

doi:10.1088/1751-8121/ac62ba

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 language	English
Article number	205202
Pages (from-to)	1-20
Number of pages	20
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	55
Issue number	20
DOIs	https://doi.org/10.1088/1751-8121/ac62ba
Publication status	Published - 20 Apr 2022

Keywords

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

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10.1088/1751-8121/ac62baLicence: CC BY

Final_Version
© 2022 The Author(s). Published by IOP Publishing Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/
Final published version, 885 KBLicence: CC BY

Cite this

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KW - scattering amplitudes

KW - positive geometries

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

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