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Article Dans Une Revue Journal of High Energy Physics Année : 2020

From positive geometries to a coaction on hypergeometric functions

Samuel Abreu
  • Fonction : Auteur
Claude Duhr
  • Fonction : Auteur
Einan Gardi
  • Fonction : Auteur
James Matthew
  • Fonction : Auteur

Résumé

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 $_{p+1}$F$_{p}$ and Appell functions.

Dates et versions

hal-02350159 , version 1 (05-11-2019)

Identifiants

Citer

Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi, James Matthew. From positive geometries to a coaction on hypergeometric functions. Journal of High Energy Physics, 2020, 02, pp.122. ⟨10.1007/JHEP02(2020)122⟩. ⟨hal-02350159⟩
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