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Tropical Grassmannians, cluster algebras and scattering amplitudes

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arxiv 1907.01053 v2 pith:COAYEHQX submitted 2019-07-01 hep-th

James Drummond , Jack Foster , Ömer Gürdoğan , Chrysostomos Kalousios This is my paper
classification hep-th
keywords amplitudesclustergrassmanniansscatteringtropicalalgebraalgebrasamplitude
verification ladder T0 review T1 audit T2 compute T3 formal
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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 ${\rm Gr}(k,n)$. 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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    Boundary structure of negative geometries, combined with Landau analysis, determines physical singularities and yields symbol alphabets for six-point two-loop and five-point three-loop ladder integrals in planar N=4 s...

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