Cluster Algebras for Feynman Integrals

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...