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arXiv · 2603.03425

Combinatorics of the Cosmohedron

Federico Ardila-Mantilla·Nima Arkani-Hamed·Carolina Figueiredo·Francisco Vazão
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Abstract

The cosmohedron was recently proposed as a polytope underlying the cosmological wavefunction for $\text{Tr}(\Phi^3)$ theory. Its faces were conjectured to be in bijection with Matryoshkas, which are obtained from a subdivision of a polygon by sequentially wrapping groups of polygons into larger polygons. In this paper we prove the correctness of this construction, and elucidate its combinatorial structure. Cosmohedra generalize to a wider class of $\mathcal{X}$ in $Y$ polytopes, where we chisel a polytope from the family $\mathcal{X}$ at each vertex of a polytope $Y$. We sketch a new application of these chiseled polytopes to the physics of ultraviolet divergences in loop-integrated Feynman amplitudes.

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Federico Ardila-Mantilla, Nima Arkani-Hamed, Carolina Figueiredo, Francisco Vazão. 2026-03-03. Combinatorics of the Cosmohedron. https://arxiv.org/abs/2603.03425

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