Feynman integrals in two dimensions and single-valued hypergeometric functions

Abstract

We show that all Feynman integrals in two Euclidean dimensions with massless propagators and arbitrary non-integer propagator powers can be expressed in terms of single-valued analogues of Aomoto-Gelfand hypergeometric functions. The latter can themselves be written as bilinears of hypergeometric functions, with coefficients that are intersection numbers in a twisted homology group. As an application, we show that all one-loop integrals in two dimensions with massless propagators can be written in terms of Lauricella $F_D^{(r)}$ functions, while the $L$-loop ladder integrals are related to the generalised hypergeometric ${}_{L+1}F_L$ functions.