Positive Geometry of Yang-Mills Correlators
Abstract
We develop a positive-geometric formulation of tree-level Yang-Mills correlators in de Sitter space at three and four points through their helicity-stripped representatives on the cosmological Grassmannian. In its Pfaffian (or spinor) embedding, physical singularities become natural geometric boundaries. At three points, the Yang-Mills correlator is the canonical form of the non-negative orthant in the Grassmannian. At four points, the Mandelstam divisors partition the Pfaffian-positive domain of the Grassmannian into four positive geometries. Requiring factorization into three-point forms, together with the correct flat-space limit, uniquely selects an oriented union of two of these regions, whose canonical form reproduces the reduced color-ordered Yang-Mills correlator. The full color-ordered correlator, on the other hand, arises from a uniquely fixed signed linear combination of homology cycles. Thus, the broader homological formulation of positive geometry is essential for capturing the complete four-point result. Our construction provides a concrete starting point for a geometric description of higher-point cosmological correlators.
Related
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BibTeX
@misc{arundine2026positive,
title = {{Positive Geometry of Yang-Mills Correlators}},
author = {Mattia Arundine and Veronica Calvo Cortes and Joris Koefler and Facundo Rost},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27594},
eprint = {2608.27594},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27594},
}
RIS
TY - UNPB
TI - Positive Geometry of Yang-Mills Correlators
AU - Mattia Arundine
AU - Veronica Calvo Cortes
AU - Joris Koefler
AU - Facundo Rost
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27594
UR - https://arxiv.org/abs/2608.27594
AB - We develop a positive-geometric formulation of tree-level Yang-Mills correlators in de Sitter space at three and four points through their helicity-stripped representatives on the cosmological Grassmannian. In its Pfaffian (or spinor) embedding, physical singularities become natural geometric boundaries. At three points, the Yang-Mills correlator is the canonical form of the non-negative orthant in the Grassmannian. At four points, the Mandelstam divisors partition the Pfaffian-positive domain of the Grassmannian into four positive geometries. Requiring factorization into three-point forms, together with the correct flat-space limit, uniquely selects an oriented union of two of these regions, whose canonical form reproduces the reduced color-ordered Yang-Mills correlator. The full color-ordered correlator, on the other hand, arises from a uniquely fixed signed linear combination of homology cycles. Thus, the broader homological formulation of positive geometry is essential for capturing the complete four-point result. Our construction provides a concrete starting point for a geometric description of higher-point cosmological correlators.
ER -