Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction

Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.
Original languageEnglish
Article number051601
JournalPhysical Review Letters
Early online date31 Jul 2017
Publication statusPublished - 4 Aug 2017

Keywords / Materials (for Non-textual outputs)

  • hep-th
  • hep-ph
  • math-ph
  • math.MP
  • math.NT


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