Tropical Grassmannians, cluster algebras and scattering amplitudes

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Abstract

We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians Gr(k, n). A finite cluster algebra provides a natural triangulation for the tropical Grassmannian whose volume computes the scattering amplitudes. Using this method one can construct the entire colour-ordered amplitude via mutations starting from a single term.

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Drummond, J., Foster, J., Gürdoğan, Ö., & Kalousios, C. (2020). Tropical Grassmannians, cluster algebras and scattering amplitudes. Journal of High Energy Physics, 2020(4). https://doi.org/10.1007/JHEP04(2020)146

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