From positive geometries to a coaction on hypergeometric functions
Citation:
Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi, James Matthew, From positive geometries to a coaction on hypergeometric functions, Journal of High Energy Physics, 2020Download Item:
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 expo- nents 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.
Sponsor
Grant Number
European Research Council (ERC)
647356
European Research Council (ERC)
637019
Other
Author's Homepage:
http://people.tcd.ie/brittorDescription:
PUBLISHED
Author: Britto, Ruth
Type of material:
Journal ArticleSeries/Report no:
Journal of High Energy PhysicsAvailability:
Full text availableKeywords:
Scattering Amplitudes, Perturbative QCDSubject (TCD):
Algebra , Theoretical PhysicsDOI:
https://doi.org/10.1007/JHEP02(2020)122ISSN:
1029-8479Metadata
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