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Adjoints and Canonical Forms of Tree Amplituhedra

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arxiv 2402.06527 v1 pith:WOP3GDHK submitted 2024-02-09 math.AG hep-th

Kristian Ranestad , Rainer Sinn , Simon Telen This is my paper · ORCID
classification math.AGhep-th
keywords amplituhedratreecanonicaladjointadjointsamplitudesarisecalled
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We consider semi-algebraic subsets of the Grassmannian of lines in three-space called tree amplituhedra. These arise in the study of scattering amplitudes from particle physics. Our main result states that tree amplituhedra in ${\rm Gr}(2,4)$ are positive geometries. The numerator of their canonical form plays the role of the adjoint in Wachspress geometry, and is uniquely determined by explicit interpolation conditions.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Canonical Forms as Dual Volumes

    hep-th 2025-09 conditional novelty 7.0 of 10

    Canonical functions of a class of positive geometries are Laplace transforms of positive measures on the dual cone, with hyperbolicity of the algebraic boundary as the characterizing property, computed explicitly in t...

  2. Geometric Landau Analysis and Symbol Bootstrap

    hep-th 2025-08 unverdicted novelty 7.0 of 10

    Boundary structure of negative geometries, combined with Landau analysis, determines physical singularities and yields symbol alphabets for six-point two-loop and five-point three-loop ladder integrals in planar N=4 s...

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