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

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2020-06-17 DOI:10.4310/atmp.2021.v25.n2.a1
S. Alexandrov
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引用次数: 7

Abstract

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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秩$N$ vfa - witten不变量,模块化和爆破
我们导出了精炼vfa - witten不变量的生成函数的显式表达式 $\Omega(\gamma,y)$ 的 $\mathbb{P}^2$ 任意阶的 $N$ 以及它们的非全纯模补全。在推导过程中,我们还提供了:i)对最近发现的的生成函数的推广 $\Omega(\gamma,y)$ 模空间的正则腔中的Hirzebruch曲面和del Pezzo曲面及其补全;Ii)直接用这些生成函数表示的放大公式的一个版本,并将其以明显的模形式重新表述。
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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