Cuts and isogenies

Hjalte Frellesvig*, Cristian Vergu, Matthias Volk, Matt von Hippel

*Corresponding author for this work

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9 Citations (Scopus)
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Abstract

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.

Original languageEnglish
Article number064
JournalJournal of High Energy Physics
Volume2021
Issue number5
Number of pages27
ISSN1029-8479
DOIs
Publication statusPublished - 10 May 2021

Keywords

  • Scattering Amplitudes
  • Differential and Algebraic Geometry
  • 2-LOOP SELF-ENERGIES
  • DIFFERENTIAL-EQUATIONS
  • FEYNMAN-INTEGRALS
  • ELLIPTIC POLYLOGARITHMS
  • ITERATED INTEGRALS
  • SUNRISE
  • DIAGRAMS
  • SPACE
  • SERIES
  • GRAPH

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