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        Momentum Amplituhedron meets Kinematic Associahedron

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        Damgaard2021_Article_MomentumAmplituhedronMeetsKine.pdf (PDF, 411Kb)
        Author
        Damgaard, David
        Ferro, Livia
        Lukowski, Tomasz
        Moerman, Robert
        Attention
        2299/24039
        Abstract
        In this paper we study a relation between two positive geometries: the momen- tum amplituhedron, relevant for tree-level scattering amplitudes in N = 4 super Yang-Mills theory, and the kinematic associahedron, encoding tree-level amplitudes in bi-adjoint scalar φ 3 theory. We study the implications of restricting the latter to four spacetime dimensions and give a direct link between its canonical form and the canonical form for the momentum amplituhedron. After removing the little group scaling dependence of the gauge theory, we find that we can compare the resulting reduced forms with the pull-back of the associahedron form. In particular, the associahedron form is the sum over all helicity sectors of the reduced momentum amplituhedron forms. This relation highlights the common sin- gularity structure of the respective amplitudes; in particular, the factorization channels, corresponding to vanishing planar Mandelstam variables, are the same. Additionally, we also find a relation between these canonical forms directly on the kinematic space of the scalar theory when reduced to four spacetime dimensions by Gram determinant constraints. As a by-product of our work we provide a detailed analysis of the kinematic spaces relevant for the four-dimensional gauge and scalar theories, and provide direct links between them.
        Publication date
        2021-02-03
        Published in
        Journal of High Energy Physics
        Published version
        https://doi.org/10.1007/jhep02(2021)041
        Other links
        http://hdl.handle.net/2299/24039
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