Bilinear tau forms of quantum Painlevé equations and $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations in SUSY gauge theories
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909979185774592 |
|---|---|
| author | Bonelli, Giulio Shchechkin, Anton Tanzini, Alessandro |
| author_facet | Bonelli, Giulio Shchechkin, Anton Tanzini, Alessandro |
| contents | We derive bilinear tau forms of the canonically quantized Painlevé equations, thereby relating them to those previously obtained from the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations for the $\mathcal{N}=2$ supersymmetric gauge theory partition functions on a general $Ω$-background. We fully fix the refined Painlevé/gauge theory dictionary by formulating the proper equations for the quantum nonautonomous Painlevé Hamiltonians. We also describe the symmetry structure of the quantum Painlevé tau functions and, as a byproduct of this analysis, obtain the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations in the nontrivial holonomy sector of the gauge theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_25051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bilinear tau forms of quantum Painlevé equations and $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations in SUSY gauge theories Bonelli, Giulio Shchechkin, Anton Tanzini, Alessandro Mathematical Physics High Energy Physics - Theory Quantum Algebra Exactly Solvable and Integrable Systems We derive bilinear tau forms of the canonically quantized Painlevé equations, thereby relating them to those previously obtained from the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations for the $\mathcal{N}=2$ supersymmetric gauge theory partition functions on a general $Ω$-background. We fully fix the refined Painlevé/gauge theory dictionary by formulating the proper equations for the quantum nonautonomous Painlevé Hamiltonians. We also describe the symmetry structure of the quantum Painlevé tau functions and, as a byproduct of this analysis, obtain the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations in the nontrivial holonomy sector of the gauge theory. |
| title | Bilinear tau forms of quantum Painlevé equations and $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations in SUSY gauge theories |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Algebra Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2512.25051 |