Modularity of Feynman Integrals and Factorization of Appell F2 Systems
Murad Alim, Filippo La Mantia
TL;DR
This paper proves the modularity of a specific Feynman integral by factorizing its Picard-Fuchs system into hypergeometric components, linking quantum field theory and algebraic geometry.
Contribution
It provides a rigorous mathematical proof of the modularity of the conformal traintrack integral using a novel factorization approach of its differential system.
Findings
Proof of modularity for the two-dimensional conformal traintrack integral.
Factorization of the Picard-Fuchs system into hypergeometric systems.
Application of gauge transformation techniques to Feynman integrals.
Abstract
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.
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