Complex crystallographic reflection groups and Seiberg-Witten integrable systems: rank 1 case
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910052027203584 |
|---|---|
| author | Argyres, Philip C. Chalykh, Oleg Lü, Yongchao |
| author_facet | Argyres, Philip C. Chalykh, Oleg Lü, Yongchao |
| contents | We consider generalisations of the elliptic Calogero--Moser systems associated to complex crystallographic groups in accordance to [1]. In our previous work [2], we proposed these systems as candidates for Seiberg--Witten integrable systems of certain SCFTs. Here we examine that proposal for complex crystallographic groups of rank one. Geometrically, this means considering elliptic curves $T^2$ with $\mathbb{Z}_m$-symmetries, $m=2,3,4,6$, and Poisson deformations of the orbifolds $(T^2\times\mathbb{C})/\mathbb{Z}_m$. The $m=2$ case was studied in [2], while $m=3,4,6$ correspond to Seiberg--Witten integrable systems for the rank 1 Minahan--Nemeshansky SCFTs of type $E_{6,7,8}$. This allows us to describe the corresponding elliptic fibrations and the Seiberg--Witten differential in a compact elegant form. This approach also produces quantum spectral curves for these SCFTs, which are given by Fuchsian ODEs with special properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12760 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Complex crystallographic reflection groups and Seiberg-Witten integrable systems: rank 1 case Argyres, Philip C. Chalykh, Oleg Lü, Yongchao High Energy Physics - Theory Mathematical Physics Representation Theory Exactly Solvable and Integrable Systems We consider generalisations of the elliptic Calogero--Moser systems associated to complex crystallographic groups in accordance to [1]. In our previous work [2], we proposed these systems as candidates for Seiberg--Witten integrable systems of certain SCFTs. Here we examine that proposal for complex crystallographic groups of rank one. Geometrically, this means considering elliptic curves $T^2$ with $\mathbb{Z}_m$-symmetries, $m=2,3,4,6$, and Poisson deformations of the orbifolds $(T^2\times\mathbb{C})/\mathbb{Z}_m$. The $m=2$ case was studied in [2], while $m=3,4,6$ correspond to Seiberg--Witten integrable systems for the rank 1 Minahan--Nemeshansky SCFTs of type $E_{6,7,8}$. This allows us to describe the corresponding elliptic fibrations and the Seiberg--Witten differential in a compact elegant form. This approach also produces quantum spectral curves for these SCFTs, which are given by Fuchsian ODEs with special properties. |
| title | Complex crystallographic reflection groups and Seiberg-Witten integrable systems: rank 1 case |
| topic | High Energy Physics - Theory Mathematical Physics Representation Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2309.12760 |