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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 oneloop 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 wellknown 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 language  English 

Article number  122 
Journal  Journal of High Energy Physics 
DOIs  
Publication status  Published  20 Feb 2020 
Keywords
 hepth
 mathph
 math.MP
 math.NT
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Projects
 1 Active

Particle Theory at the Higgs Centre
Ball, R., Boyle, P., Del Debbio, L., Gardi, E., Horsley, R., Kennedy, A., O'Connell, D., Smillie, J. & Zwicky, R.
1/10/17 → 30/09/21
Project: Research