From positive geometries to a coaction on hypergeometric functions

Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi, James Matthew

Research output: Contribution to journalArticlepeer-review

Abstract

It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on one-loop Feynman integrals in dimensional regularization, we use intersection numbers and twisted homology theory to define a coaction on certain hypergeometric functions. The functions we consider admit an integral representation where both the integrand and the contour of integration are associated with positive geometries. As in dimensionally- regularized Feynman integrals, endpoint singularities are regularized by means of exponents controlled by a small parameter ϵ. We show that the coaction defined on this class of integral is consistent, upon expansion in ϵ, with the well-known coaction on multiple polylogarithms. We illustrate the validity of our construction by explicitly determining the coaction on various types of hypergeometric p+1Fp and Appell functions.
Original languageEnglish
Article number122
Journal Journal of High Energy Physics
DOIs
Publication statusPublished - 20 Feb 2020

Keywords

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

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