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The m=2 amplituhedron

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arxiv 1909.06015 v2 pith:6QJFY5F5 submitted 2019-09-13 math.CO hep-thmath.RT

Huanchen Bao , Xuhua He This is my paper · ORCID
classification math.COhep-thmath.RT
keywords amplituhedronmathcaladmitsarkani-hamedbcfw-typecellscollectionconstructed
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

The (tree) amplituhedron $\mathcal{A}_{n, k, m}$ is introduced by Arkani-Hamed and Trnka in 2013 in the study of $\mathcal{N}=4$ supersymmetric Yang-Mills theory. It is defined in terms of the totally nonnegative Grassmannians. In this paper, we show that the amplituhedron $\mathcal{A}_{n, k, m}$ for $m=2$ admits a triangulation. Our collection of cells is constructed via BCFW-type recursion. We also provide a diagrammatic interpretation of our construction.

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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. Notes on the one-loop amplituhedron and its BCFW tiling

    math-ph 2025-06 conditional novelty 7.0 of 10

    The one-loop amplituhedron is tiled by BCFW cells, extending the author's tree-level proof of the BCFW tiling conjecture to one loop.

  2. Amplituhedra for generic quantum processes via the TQNN representation of UQC

    quant-ph 2025-09 reject novelty 5.0 of 10

    The paper proposes a formal correspondence between topological quantum neural networks and amplituhedra, claiming generic quantum processes have amplituhedron representations.

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