The momentum amplituhedron

DOI10.1007/JHEP08(2019)042zbMATH Open1421.81148arXiv1905.04216OpenAlexW2968108619WikidataQ127390286 ScholiaQ127390286MaRDI QIDQ2273401

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Publication date: 23 September 2019

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Abstract: In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in $mathcalN=4$ super Yang-Mills theory in spinor helicity space. Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region. The momentum amplituhedron $mathcal{M}_{n,k}$ is then the image of the positive Grassmannian via a map determined by such kinematics. The scattering amplitudes are extracted from the canonical form with logarithmic singularities on the boundaries of this geometry.

Full work available at URL: https://arxiv.org/abs/1905.04216

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