Constructs multivariate hypergeometric series for calculating conformal integrals in D dimensions, indicating a novel approach using polygons.
A bstract We explicitly construct a class of multivariate generalized hypergeometric series which is conjectured in our previous paper [1] to calculate multipoint one-loop parametric conformal integrals in D dimensions. Our approach is based on a simple diagrammatic algorithm which systematically builds both arguments and series coefficients in terms of a convex polygon which is part of the Baxter lattice. The examples of the box, pentagon, and hexagon integrals are considered in detail.
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Alkalaev et al. (2025) studied this question.
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