Rank $N$ Vafa-Witten invariants, modularity and blow-up
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2020
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915382347956224 |
|---|---|
| author | Alexandrov, Sergei |
| author_facet | Alexandrov, Sergei |
| contents | We derive explicit expressions for the generating functions of refined Vafa-Witten invariants $Ω(γ,y)$ of $\mathbb{P}^2$ of arbitrary rank $N$ and for their non-holomorphic modular completions. In the course of derivation we also provide: i) a generalization of the recently found generating functions of $Ω(γ,y)$ and their completions for Hirzebruch and del Pezzo surfaces in the canonical chamber of the moduli space to a generic chamber; ii) a version of the blow-up formula expressed directly in terms of these generating functions and its reformulation in a manifestly modular form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_10074 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Rank $N$ Vafa-Witten invariants, modularity and blow-up Alexandrov, Sergei High Energy Physics - Theory Mathematical Physics Algebraic Geometry Number Theory We derive explicit expressions for the generating functions of refined Vafa-Witten invariants $Ω(γ,y)$ of $\mathbb{P}^2$ of arbitrary rank $N$ and for their non-holomorphic modular completions. In the course of derivation we also provide: i) a generalization of the recently found generating functions of $Ω(γ,y)$ and their completions for Hirzebruch and del Pezzo surfaces in the canonical chamber of the moduli space to a generic chamber; ii) a version of the blow-up formula expressed directly in terms of these generating functions and its reformulation in a manifestly modular form. |
| title | Rank $N$ Vafa-Witten invariants, modularity and blow-up |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2006.10074 |