Solutions to Open WDVV Equations for the Universal Whitham Hierarchy
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918229705752576 |
|---|---|
| author | Ma, Shilin |
| author_facet | Ma, Shilin |
| contents | In this paper, we construct a pair of solutions to the open WDVV equations associated with the infinite-dimensional Frobenius manifolds that underlie the genus-zero universal Whitham hierarchy, and for the resulting flat F-manifolds, we explicitly construct their principal hierarchies. We further demonstrate that this construction is compatible with finite-dimensional reductions, yielding solutions for Frobenius manifolds associated with general rational superpotentials and those subject to a $\mathbb{Z}_{2}$-symmetry reduction. In particular, the polynomial solutions derived by Basalaev and Buryak via open Saito theory for A- and D-type singularities are recovered as special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solutions to Open WDVV Equations for the Universal Whitham Hierarchy Ma, Shilin Mathematical Physics Differential Geometry 53D45, 37K10 In this paper, we construct a pair of solutions to the open WDVV equations associated with the infinite-dimensional Frobenius manifolds that underlie the genus-zero universal Whitham hierarchy, and for the resulting flat F-manifolds, we explicitly construct their principal hierarchies. We further demonstrate that this construction is compatible with finite-dimensional reductions, yielding solutions for Frobenius manifolds associated with general rational superpotentials and those subject to a $\mathbb{Z}_{2}$-symmetry reduction. In particular, the polynomial solutions derived by Basalaev and Buryak via open Saito theory for A- and D-type singularities are recovered as special cases. |
| title | Solutions to Open WDVV Equations for the Universal Whitham Hierarchy |
| topic | Mathematical Physics Differential Geometry 53D45, 37K10 |
| url | https://arxiv.org/abs/2512.03455 |