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Rank $N$ Vafa-Witten invariants, modularity and blow-up 
Auteur(s): Alexandrov S.
(Article) Publié:
Advances In Theoretical And Mathematical Physics, vol. 25 p.275-308 (2022)
Texte intégral en Openaccess : 
Ref HAL: hal-02878251_v1
Ref Arxiv: 2006.10074
DOI: 10.4310/ATMP.2021.v25.n2.a1
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé: We derive explicit expressions for the generating functions of refined Vafa-Witten invariants $\Omega(\gamma,y)$ 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 $\Omega(\gamma,y)$ 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.
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