From momentum amplituhedron boundaries to amplitude singularities and back

DOI10.1007/JHEP07(2020)201zbMATH Open1451.81358arXiv2003.13704OpenAlexW3098121006MaRDI QIDQ2215430

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Publication date: 11 December 2020

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Abstract: The momentum amplituhedron is a positive geometry encoding tree-level scattering amplitudes in $mathcalN=4$ super Yang-Mills directly in spinor-helicity space. In this paper we classify all boundaries of the momentum amplituhedron $mathcal{M}_{n,k}$ and explain how these boundaries are related to the expected factorization channels, and soft and collinear limits of tree amplitudes. Conversely, all physical singularities of tree amplitudes are encoded in this boundary stratification. Finally, we find that the momentum amplituhedron $mathcal{M}_{n,k}$ has Euler characteristic equal to one, which provides a first step towards proving that it is homeomorphic to a ball.

Full work available at URL: https://arxiv.org/abs/2003.13704

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