University of Hertfordshire

By the same authors

On the Boundaries of the m=2 Amplituhedron

Research output: Contribution to journalArticle

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  • 1908.00386v1

    Accepted author manuscript, 660 KB, PDF document

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Original languageEnglish
JournalANNALES DE L’INSTITUT HENRI POINCARÉ D
Publication statusAccepted/In press - 15 Feb 2020

Abstract

Amplituhedra A_{n,k}^{(m)} are geometric objects of great interest in modern mathematics and physics: for mathematicians they are combinatorially rich generalizations of polygons and polytopes, based on the notion of positivity; for physicists, the amplituhedron A^{(4)}_{n,k} encodes the scattering amplitudes of the planar N=4 super Yang-Mills theory. In this paper we study the structure of boundaries for the amplituhedron A_{n,k}^{(2)}. We classify all boundaries of all dimensions and provide their graphical enumeration. We find that the boundary poset for the amplituhedron is Eulerian and show that the Euler characteristic of the amplituhedron equals one. This provides an initial step towards proving that the amplituhedron for m=2 is homeomorphic to a closed ball.

Notes

14 pages, 3 figures

ID: 19784434