Description
Feynman Integrals are closely linked to periods of non-trivial geometries such as Calabi-Yau manifolds, elliptic, as well as higher genus curves. Starting from the archetypical Calabi-Yau Feynman integral, the four-loop equal-mass Banana integral, we construct an associated genus-two hyperelliptic curve by performing a matching on the level of (intermediate) Jacobians. We thus show that the geometry associated to a Feynman integral is not unique, and that it is possible to explicitly construct such equivalent geometries.
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