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The algebraic structure of cut Feynman integrals and the diagrammatic coaction

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Abstract

We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It reduces to the known coaction on multiple polylogarithms, but applies more generally, e.g. to hypergeometric functions. The coaction also applies to generic one-loop Feynman integrals with any configuration of internal and external masses, and in dimensional regularization. In this case, we demonstrate that it can be given a diagrammatic representation purely in terms of operations on graphs, namely contractions and cuts of edges. The coaction gives direct access to (iterated) discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they admit. In particular, the differential equations for any one-loop integral are determined by the diagrammatic coaction using limited information about their maximal, next-to-maximal, and next-to-next-to-maximal cuts.
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cea-01491820 , version 1 (17-03-2017)

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Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi. The algebraic structure of cut Feynman integrals and the diagrammatic coaction. 2017. ⟨cea-01491820⟩
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