Feynman integrals in two dimensions and single-valued hypergeometric functions
Claude Duhr, Franziska Porkert
Abstract
A bstract 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 $$ {F}_D^{(r)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mi>D</mml:mi> <mml:mfenced> <mml:mi>r</mml:mi> </mml:mfenced> </mml:msubsup> </mml:math> functions, while the L -loop ladder integrals are related to the generalised hypergeometric L +1 F L functions.