Canonical Differential Equations Beyond Genus One
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914096464527360 |
|---|---|
| author | Duhr, Claude Porkert, Franziska Stawinski, Sven F. |
| author_facet | Duhr, Claude Porkert, Franziska Stawinski, Sven F. |
| contents | We discuss for the first time canonical differential equations for hyperelliptic Feynman integrals. We study hyperelliptic Lauricella functions that include in particular the maximal cut of the two-loop non-planar double box, which is known to involve a hyperlliptic curve of genus two. We consider specifically three- and four-parameter Lauricella functions, each associated to a hyperelliptic curve of genus two, and construct their canonical differential equations. Whilst core steps of this construction rely on existing methods $\unicode{x2014}$ that we show to be applicable in the higher-genus case $\unicode{x2014}$ we use new ideas on the structure of the twisted cohomology intersection matrix associated to the integral family in canonical form to obtain a better understanding of the appearing new functions. We further observe the appearance of Siegel modular forms in the $\varepsilon$-factorized differential equation matrix, nicely generalizing similar observations from the elliptic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Canonical Differential Equations Beyond Genus One Duhr, Claude Porkert, Franziska Stawinski, Sven F. High Energy Physics - Theory Mathematical Physics We discuss for the first time canonical differential equations for hyperelliptic Feynman integrals. We study hyperelliptic Lauricella functions that include in particular the maximal cut of the two-loop non-planar double box, which is known to involve a hyperlliptic curve of genus two. We consider specifically three- and four-parameter Lauricella functions, each associated to a hyperelliptic curve of genus two, and construct their canonical differential equations. Whilst core steps of this construction rely on existing methods $\unicode{x2014}$ that we show to be applicable in the higher-genus case $\unicode{x2014}$ we use new ideas on the structure of the twisted cohomology intersection matrix associated to the integral family in canonical form to obtain a better understanding of the appearing new functions. We further observe the appearance of Siegel modular forms in the $\varepsilon$-factorized differential equation matrix, nicely generalizing similar observations from the elliptic case. |
| title | Canonical Differential Equations Beyond Genus One |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2412.02300 |