Faces of cosmological polytopes

  • Lukas Kühne

    Universität Bielefeld, Bielefeld, Germany
  • Leonid Monin

    Swiss Federal Institute of Technology in Lausanne, Lausanne, Switzerland
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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 -vector of cosmological polytopes of trees.

Cite this article

Lukas Kühne, Leonid Monin, Faces of cosmological polytopes. Ann. Inst. Henri Poincaré Comb. Phys. Interact. (2024), published online first

DOI 10.4171/AIHPD/192