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arXiv · 2103.13908

Kleiss-Kuijf Relations from Momentum Amplituhedron Geometry

David Damgaard·Livia Ferro·Tomasz Lukowski·Robert Moerman
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Abstract

In recent years, it has been understood that color-ordered scattering amplitudes can be encoded as logarithmic differential forms on positive geometries. In particular, amplitudes in maximally supersymmetric Yang-Mills theory in spinor helicity space are governed by the momentum amplituhedron. Due to the group-theoretic structure underlying color decompositions, color-ordered amplitudes enjoy various identities which relate different orderings. In this paper, we show how the Kleiss-Kuijf relations arise from the geometry of the momentum amplituhedron. We also show how similar relations can be realised for the kinematic associahedron, which is the positive geometry of bi-adjoint scalar cubic theory.

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David Damgaard, Livia Ferro, Tomasz Lukowski, Robert Moerman. 2021-03-25. Kleiss-Kuijf Relations from Momentum Amplituhedron Geometry. https://doi.org/10.1007/jhep07(2021)111

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