%0 Journal Article
%T Rank $N$ Vafa-Witten invariants, modularity and blow-up
%+ Laboratoire Charles Coulomb (L2C)
%A Alexandrov, Sergey
%< avec comité de lecture
%Z L2C:20-057
%@ 1095-0761
%J Advances in Theoretical and Mathematical Physics
%I International Press
%V 25
%N 2
%P 275-308
%8 2022-02-17
%D 2022
%Z 2006.10074
%R 10.4310/ATMP.2021.v25.n2.a1
%Z Physics [physics]/High Energy Physics - Theory [hep-th]
%Z Physics [physics]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Algebraic Geometry [math.AG]
%Z Mathematics [math]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Number Theory [math.NT]Journal articles
%X 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.
%G English
%L hal-02878251
%U https://hal.science/hal-02878251
%~ CNRS
%~ L2C
%~ TDS-MACS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021
%~ UM-EPE