Conformal Integrals in four dimensions

TL;DR

This paper derives explicit analytic formulas for four-dimensional Euclidean N-point conformal integrals using differential equations, linking them to hypergeometric systems and expressing solutions via series in conformal cross ratios.

Contribution

It provides a novel analytic solution for N-point conformal integrals in four dimensions, connecting them to GKZ hypergeometric systems.

Findings

Explicit formulas for conformal integrals for any N

Connection to GKZ hypergeometric systems

Solutions expressed in series of conformal cross ratios

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.