Modular transformations of elliptic Feynman integrals

Abstract

We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast numerical evaluations. Contrary to the case of multiple polylogarithms, where it is sufficient to consider just variable transformations for the numerical evaluations of multiple polylogarithms, it is more natural in the elliptic case to consider a combination of a variable transformation (i.e. a modular transformation) together with a redefinition of the master integrals. Thus we combine a coordinate transformation on the base manifold with a basis transformation in the fibre. Only in the combination of the two transformations we stay within the same class of functions.

29 pages, v2: version to be published

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Cited by in corpus (19)

• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• Bananas of equal mass: any loop, any order in the dimensional regularisation parameter
• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
• The elliptic double box and symbology beyond polylogarithms
• Meromorphic modular forms and the three-loop equal-mass banana integral
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• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Cutting the traintracks: Cauchy, Schubert and Calabi-Yau
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• Massive kite diagrams with elliptics
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• A Calabi-Yau-to-Curve Correspondence for Feynman Integrals
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• Non-planar elliptic vertex
• Electroweak double-box integrals for Moller scattering
• Massive Two-Loop Heavy Particle Diagrams
• Vanishing cycles and analysis of singularities of Feynman diagrams
• Integral representation for three-loop banana graph
• A Feynman integral depending on two elliptic curves