Combinatorics of the Cosmohedron
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910061107871744 |
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| author | Ardila-Mantilla, Federico Arkani-Hamed, Nima Figueiredo, Carolina Vazão, Francisco |
| author_facet | Ardila-Mantilla, Federico Arkani-Hamed, Nima Figueiredo, Carolina Vazão, Francisco |
| contents | The cosmohedron was recently proposed as a polytope underlying the cosmological wavefunction for $\text{Tr}(Φ^3)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03425 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorics of the Cosmohedron Ardila-Mantilla, Federico Arkani-Hamed, Nima Figueiredo, Carolina Vazão, Francisco Combinatorics High Energy Physics - Theory The cosmohedron was recently proposed as a polytope underlying the cosmological wavefunction for $\text{Tr}(Φ^3)$ 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. |
| title | Combinatorics of the Cosmohedron |
| topic | Combinatorics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.03425 |