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Cuts and Isogenies

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arxiv 2102.02769 v1 pith:C5NID3GM submitted 2021-02-04 hep-th

Hjalte Frellesvig , Cristian Vergu , Matthias Volk , Matt von Hippel This is my paper · ORCID
classification hep-th
keywords curvesgenus-onecutsfeynmangeometryisogeniesarisearises
verification ladder T0 review T1 audit T2 compute T3 formal
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We consider the genus-one curves which arise in the cuts of the sunrise and in the elliptic double-box Feynman integrals. We compute and compare invariants of these curves in a number of ways, including Feynman parametrization, lightcone and Baikov (in full and loop-by-loop variants). We find that the same geometry for the genus-one curves arises in all cases, which lends support to the idea that there exists an invariant notion of genus-one geometry, independent on the way it is computed. We further indicate how to interpret some previous results which found that these curves are related by isogenies instead.

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  1. Special Fano geometry from Feynman integrals

    hep-th 2024-12 conditional novelty 5.0 of 10

    Special Fano varieties, which include Calabi-Yau spaces as the Q=1 case, arise from the Symanzik polynomials of several families of Feynman integrals.

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