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Faces of Cosmological Polytopes

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arxiv 2209.08069 v2 pith:PJEB6ZMH submitted 2022-09-16 math.CO hep-th

Lukas Kühne , Leonid Monin This is my paper · ORCID
classification math.COhep-th
keywords cosmologicalfacespolytopepolytopesdescriptiongivearkani-hamedbenincasa
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abstract

A cosmological polytope is a lattice polytope introduced by Arkani-Hamed, Benincasa, and Postnikov in their study of the wavefunction of the universe in a class of cosmological models. More concretely, they construct a cosmological polytope for any Feynman diagram, i.e. an undirected graph. In this paper, we initiate a combinatorial study of these polytopes. We give a complete description of their faces, identify minimal faces that are not simplices and compute the number of faces in specific instances. In particular, we give a recursive description of the $f$-vector of cosmological polytopes of trees.

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  1. Euler Discriminant of Complements of Hyperplanes

    math.AG 2024-11 conditional novelty 7.0 of 10

    The Euler discriminant of families of hyperplane complements is the zero set of an explicit product of determinants indexed by connected square subgraphs.

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