Good triangulations of cosmological polytopes
File(s)
Published version
Author(s)
Benjes, Aenne
Ferry, Kamillo
Schröter, Benjamin
Type
Journal Article
Abstract
Cosmological polytopes of graphs are a geometric tool in physics to study wavefunctions for cosmological models whose Feynman diagram is given by the graph. After their recent introduction by Arkani-Hamed, Benincasa, and Postnikov, the focus of interest shifted towards their mathematical properties, for example, their face structure and triangulations. Juhnke, Solus, and Venturello used toric geometry to show that these polytopes have a so-called good triangulation that is unimodular. Based on these results, Bruckamp et al. studied the Ehrhart theory of those polytopes and in particular the $h^{*}$-polynomials of cosmological polytopes of multitrees and multicycles. In this article, we complete this part of the story. We enumerate all maximal simplices in good triangulations of any cosmological polytope, hence finding a formula for their volume. Furthermore, we provide a method to turn such a triangulation into a half-open decomposition from which we deduce that the $h^{*}$-polynomial of a cosmological polytope is a specialization of the Tutte polynomial of the defining graph. This settles several open questions and conjectures of Juhnke, Solus, and Venturello as well as Bruckamp et al.
Date Issued
2025-11-01
Date Acceptance
2025-10-08
Citation
International Mathematics Research Notices, 2025, 2025 (21)
ISSN
1073-7928
Publisher
Oxford University Press (OUP)
Journal / Book Title
International Mathematics Research Notices
Volume
2025
Issue
21
License URL
Publication Status
Published
Article Number
rnaf332
Date Publish Online
2025-10-30