Modularity of Feynman Integrals and Factorization of Appell F2 Systems

Certain Feynman integrals can be expressed as periods of differential forms on Calabi–Yau manifolds. We provide a mathematical proof of a result of Duhr and Maggio on the modularity of the two-dimensional conformal traintrack integral. Our approach is based on a factorization of the associated Picard-Fuchs system into a tensor product of Gauss hypergeometric systems via a gauge transformation due to Clingher, Doran and Malmendier.