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 super Yang-Mills.
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 ${\rm Gr}(k,n)$. 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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Geometric Landau Analysis and Symbol Bootstrap
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 super Yang-Mills.