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Article Dans Une Revue Advances in Theoretical and Mathematical Physics Année : 2022

Rank $N$ Vafa-Witten invariants, modularity and blow-up

Sergey Alexandrov
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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.

Dates et versions

hal-02878251 , version 1 (23-06-2020)

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Citer

Sergey Alexandrov. Rank $N$ Vafa-Witten invariants, modularity and blow-up. Advances in Theoretical and Mathematical Physics, 2022, 25 (2), pp.275-308. ⟨10.4310/ATMP.2021.v25.n2.a1⟩. ⟨hal-02878251⟩
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