PreprintCC BY 4.0arXiv
The m=2 amplituhedron is a positive geometry
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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BibTeX
@misc{koefler2026amplituhedron,
title = {{The $m=2$ amplituhedron is a positive geometry}},
author = {Joris Koefler and Dmitrii Pavlov and Rainer Sinn},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27903},
eprint = {2610.27903},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27903},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The m=2 amplituhedron is a positive geometry
AU - Joris Koefler
AU - Dmitrii Pavlov
AU - Rainer Sinn
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27903
UR - https://arxiv.org/abs/2610.27903
AB - 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.
ER -