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.
Type de document :
Pré-publication, Document de travail
t17/042 2017
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Contributeur : Emmanuelle De Laborderie <>
Soumis le : vendredi 17 mars 2017 - 14:12:25
Dernière modification le : mercredi 23 janvier 2019 - 14:39:04
Document(s) archivé(s) le : dimanche 18 juin 2017 - 13:25:19


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


Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi. The algebraic structure of cut Feynman integrals and the diagrammatic coaction. t17/042 2017. 〈cea-01491820〉



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