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arXiv · 2404.05785

A Calabi-Yau-to-Curve Correspondence for Feynman Integrals

Hans Jockers·Sören Kotlewski·Pyry Kuusela·Andrew J. McLeod·Sebastian Pögel·Maik Sarve·Xing Wang·Stefan Weinzierl
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Abstract

It has long been known that the maximal cut of the equal-mass four-loop banana integral is a period of a family of Calabi-Yau threefolds that depends on the kinematic variable $z=m^2/p^2$. We show that it can also be interpreted as a period of a family of genus-two curves. We do this by introducing a general Calabi-Yau-to-curve correspondence, which in this case locally relates the original period of the family of Calabi-Yau threefolds to a period of a family of genus-two curves that varies holomorphically with the kinematic variable $z$. In addition to working out the concrete details of this correspondence for the equal-mass four-loop banana integral, we outline when we expect a correspondence of this type to hold.

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Hans Jockers, Sören Kotlewski, Pyry Kuusela, Andrew J. McLeod, Sebastian Pögel, Maik Sarve, Xing Wang, Stefan Weinzierl. 2025-01-10. A Calabi-Yau-to-Curve Correspondence for Feynman Integrals. https://doi.org/10.1007/jhep01(2025)030

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