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- W3135635141 abstract "We initiate the study of cluster algebras in Feynman integrals in dimensional regularization. We provide evidence that four-point Feynman integrals with one off-shell leg are described by a ${C}_{2}$ cluster algebra, and we find cluster adjacency relations that restrict the allowed function space. By embedding ${C}_{2}$ inside the ${A}_{3}$ cluster algebra, we identify these adjacencies with the extended Steinmann relations for six-particle massless scattering. The cluster algebra connection we find restricts the functions space for vector boson or Higgs plus jet amplitudes and for form factors recently considered in $mathcal{N}=4$ super Yang-Mills. We explain general procedures for studying relationships between alphabets of generalized polylogarithmic functions and cluster algebras and use them to provide various identifications of one-loop alphabets with cluster algebras. In particular, we show how one can obtain one-loop alphabets for five-particle scattering from a recently discussed dual conformal eight-particle alphabet related to the $G(4,8)$ cluster algebra." @default.
- W3135635141 created "2021-03-15" @default.
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- W3135635141 date "2021-03-05" @default.
- W3135635141 modified "2023-10-11" @default.
- W3135635141 title "Cluster Algebras for Feynman Integrals" @default.
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- W3135635141 doi "https://doi.org/10.1103/physrevlett.126.091603" @default.
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