From positive geometries to a coaction on hypergeometric functions

Understand

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 $\epsilon$.