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arXiv · 2610.27903

The $m=2$ amplituhedron is a positive geometry

Joris Koefler·Dmitrii Pavlov·Rainer Sinn
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Abstract

Amplituhedra are semi-algebraic sets of fundamental importance in particle physics. Their discovery initiated the field of Positive Geometry. We settle a central conjecture in this field: we show that the $m=2$ amplituhedron is a positive geometry. Our main new tool is a Hodge-theoretic criterion for being a positive geometry, connecting the work of Brown--Dupont with the original setup of Arkani-Hamed--Bai--Lam.

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Joris Koefler, Dmitrii Pavlov, Rainer Sinn. 2026-10-20. The $m=2$ amplituhedron is a positive geometry. https://arxiv.org/abs/2610.27903

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