Conformal Integrals in four dimensions

Abstract

We obtain analytic expressions of four-dimensional Euclidean $N$-point conformal integrals for arbitrary $N$ by solving a Lauricella-like system of differential equations derived earlier. We demonstrate their relation to the GKZ A-hypergeometric systems. The conformal integrals are solutions to these expressed in terms of leg factors and infinite series in the conformal invariant cross ratios.