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arXiv · 2012.12285

Cluster algebras for Feynman integrals

Dmitry Chicherin·Johannes M. Henn·Georgios Papathanasiou
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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.

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Dmitry Chicherin, Johannes M. Henn, Georgios Papathanasiou. 2020-12-22. Cluster algebras for Feynman integrals. https://doi.org/10.1103/physrevlett.126.091603

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