论文标题
来自模块化异常的VAFA字体不变
Vafa-Witten invariants from modular anomaly
论文作者
论文摘要
最近，已经提出了一种通用公式，用于在各种理论中具有$ n = 2 $ supersymmemery的各种理论中精制BPS索引的生成函数的非形态模块化完成。它通过较低等级的全体形态生成功能表示完成。在这里，我们表明，对于$ u（n）$ vafa，关于Hirzebruch和del pezzo表面的理论，该公式可用于提取霍明型功能本身，从而在此类表面上提供了Betti数量的Instanton Moduli空间。结果，我们为生成功能提供了一个封闭的公式及其完成的所有$ n $。此外，我们的构造以简单的方式揭示了光纤二元性的实例，该实例可用于为广义的Appell函数得出新的非平凡身份。这也暗示了新不变的存在，但其含义仍然晦涩难懂。
Recently, a universal formula for a non-holomorphic modular completion of the generating functions of refined BPS indices in various theories with $N=2$ supersymmetry has been suggested. It expresses the completion through the holomorphic generating functions of lower ranks. Here we show that for $U(N)$ Vafa-Witten theory on Hirzebruch and del Pezzo surfaces this formula can be used to extract the holomorphic functions themselves, thereby providing the Betti numbers of instanton moduli spaces on such surfaces. As a result, we derive a closed formula for the generating functions and their completions for all $N$. Besides, our construction reveals in a simple way instances of fiber-base duality, which can be used to derive new non-trivial identities for generalized Appell functions. It also suggests the existence of new invariants, whose meaning however remains obscure.
