Modularity of Feynman Integrals and Factorization of Appell F2 Systems

Murad Alim; Filippo La Mantia

doi:10.1016/j.geomphys.2026.105906

Modularity of Feynman Integrals and Factorization of Appell F2 Systems

Murad Alim
, Filippo La Mantia

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	105906
Journal	Journal of Geometry and Physics
Volume	228
Early online date	8 Jun 2026
DOIs	https://doi.org/10.1016/j.geomphys.2026.105906
Publication status	Published - Oct 2026

Keywords

Calabi-Yau periods
Feynman integrals
Hypergeometric functions
K3 surfaces
Modular forms
Picard-Fuchs systems

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

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10.1016/j.geomphys.2026.105906

Cite this

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title = "Modularity of Feynman Integrals and Factorization of Appell F2 Systems",

abstract = "Certain Feynman integrals can be expressed as periods of differential forms on Calabi{\textendash}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.",

keywords = "Calabi-Yau periods, Feynman integrals, Hypergeometric functions, K3 surfaces, Modular forms, Picard-Fuchs systems",

author = "Murad Alim and \{La Mantia\}, Filippo",

year = "2026",

month = oct,

doi = "10.1016/j.geomphys.2026.105906",

language = "English",

volume = "228",

journal = "Journal of Geometry and Physics",

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AU - Alim, Murad

AU - La Mantia, Filippo

PY - 2026/10

Y1 - 2026/10

N2 - 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.

AB - 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.

KW - Calabi-Yau periods

KW - Feynman integrals

KW - Hypergeometric functions

KW - K3 surfaces

KW - Modular forms

KW - Picard-Fuchs systems

UR - https://www.scopus.com/pages/publications/105041194076

U2 - 10.1016/j.geomphys.2026.105906

DO - 10.1016/j.geomphys.2026.105906

M3 - Article

SN - 0393-0440

VL - 228

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

M1 - 105906

ER -

Modularity of Feynman Integrals and Factorization of Appell F2 Systems

Abstract

Keywords

ASJC Scopus subject areas

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