|XXXIX Workshop on Geometric Methods in Physics||27.06-3.07.2021|
|IX School on Geometry and Physics||21-25.06.2021|
Scattering Amplitudes as Generalized Associahedra
A new construction of the associahedron was recently given by Arkani-Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. This is a geometric realization in certain quantum field theories which simplifies complicated computation by Feynman diagrams. Via represenation theory, we show that their construction (suitably understood) can be applied to construct generalized associahedra of any simply-laced Dynkin type. Unexpectedly, we also show that this same construction produces Newton polytopes for all the F-polynomials of the corresponding cluster algebras.
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