Cuts and Isogenies
High Energy Physics - Theory
2021-05-26 v1
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.
Keywords
Cite
@article{arxiv.2102.02769,
title = {Cuts and Isogenies},
author = {Hjalte Frellesvig and Cristian Vergu and Matthias Volk and Matt von Hippel},
journal= {arXiv preprint arXiv:2102.02769},
year = {2021}
}
Comments
24 pages, 2 figures