Work

The $m=2$ amplituhedron is a positive geometry

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27903

Authors: Koefler, Joris, Pavlov, Dmitrii, Sinn, Rainer

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Deutsche Forschungsgemeinschaft, Universität Wien, Erwin Schrödinger International Institute for Mathematics and Physics

Awards: G5893294622, G8284209191, Positive Geometrie

OpenAlex ID: W7223159099

Cites: 11

Cited by: 1

Related to: 10