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

15 Jul 2021  ·  Tomasz Lukowski, Jonah Stalknecht ·

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. read more

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High Energy Physics - Theory Algebraic Geometry