On the geometry of the orthogonal momentum amplituhedron

A bstract In this paper we focus on the orthogonal momentum amplituhedron O k , a recently introduced positive geometry that encodes the tree-level scattering amplitudes in ABJM theory. We generate the full boundary stratification of O k for various k and conjecture that its boundaries can be labell...

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Published inThe journal of high energy physics Vol. 2022; no. 12; pp. 6 - 26
Main Authors Łukowski, Tomasz, Moerman, Robert, Stalknecht, Jonah
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2022
Springer Nature B.V
SpringerOpen
Subjects
Classical and Quantum Gravitation
Elementary Particles
Forests
Geometry
Graphs
High energy physics
Momentum
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scattering Amplitudes
Set theory
String Theory
Supersymmetric Gauge Theory
Scattering Amplitudes
Supersymmetric Gauge Theory
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Summary:A bstract In this paper we focus on the orthogonal momentum amplituhedron O k , a recently introduced positive geometry that encodes the tree-level scattering amplitudes in ABJM theory. We generate the full boundary stratification of O k for various k and conjecture that its boundaries can be labelled by so-called orthogonal Grassmannian forests (OG forests). We determine the generating function for enumerating these forests according to their dimension and show that the Euler characteristic of the poset of these forests equals one. This provides a strong indication that the orthogonal momentum amplituhedron is homeomorphic to a ball. This paper is supplemented with the M athematica package orthitroids which contains useful functions for exploring the structure of the positive orthogonal Grassmannian and the orthogonal momentum amplituhedron.
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP12(2022)006