Amplituhedra and origami, I: tree level

Pavel Galashin

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arXiv · 2410.09574

Amplituhedra and origami, I: tree level

Pavel Galashin

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Abstract

We establish a precise correspondence between points of the $m=4$ tree momentum amplituhedron and origami crease patterns. As an application, we prove that the BCFW (Britto-Cachazo-Feng-Witten) cells triangulate the $m=4$ tree amplituhedron both in momentum space and in momentum-twistor space. As another application, we show that every nondegenerate weighted planar bipartite graph $\Gamma$ admits a t-embedding, i.e., an embedding of the planar dual of $\Gamma$ such that the sum of angles of white (equivalently, black) faces around each vertex is equal to $\pi$.

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Pavel Galashin. 2024-10-12. Amplituhedra and origami, I: tree level. https://arxiv.org/abs/2410.09574

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