The algebraic structure of cut Feynman integrals and the diagrammatic coaction

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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https://hal-cea.archives-ouvertes.fr/cea-01491820
Contributor : Emmanuelle de Laborderie <>
Submitted on : Friday, March 17, 2017 - 2:12:25 PM
Last modification on : Thursday, May 2, 2019 - 2:16:11 PM
Long-term archiving on : Sunday, June 18, 2017 - 1:25:19 PM

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  • HAL Id : cea-01491820, version 1
  • ARXIV : 1703.05064

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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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