论文标题
从量子曲线到拓扑弦分区函数II
From quantum curves to topological string partition functions II
论文作者
论文摘要
我们提出了与$ d = 4 $，$ \ Mathcal {n} = 2 $ supersymmetric Field的几何工程中使用的本地Calabi-yau（CY）歧管相关的拓扑字符串分区功能的几何表征。这些CY歧管的定量定义了称为量子曲线的差分运算符。分区函数是从与量子曲线相关的异构质tau函数中提取的，该功能是通过广义theta序列类型的扩展。事实证明，使用精确WKB方法定义的量子曲线的模量空间上，分区函数与首选坐标的一对一对应关系。以这种方式定义的坐标跳过模量空间中的某些基因座。与这些跳跃相关的tau功能的归一化变化定义了自然线束在此处提出的拓扑字符串分区函数的几何表征中起关键作用。
We propose a geometric characterisation of the topological string partition functions associated to the local Calabi-Yau (CY) manifolds used in the geometric engineering of $d=4$, $\mathcal{N}=2$ supersymmetric field theories of class $\mathcal{S}$. A quantisation of these CY manifolds defines differential operators called quantum curves. The partition functions are extracted from the isomonodromic tau-functions associated to the quantum curves by expansions of generalised theta series type. It turns out that the partition functions are in one-to-one correspondence with preferred coordinates on the moduli spaces of quantum curves defined using the Exact WKB method. The coordinates defined in this way jump across certain loci in the moduli space. The changes of normalisation of the tau-functions associated to these jumps define a natural line bundle playing a key role in the geometric characterisation of the topological string partition functions proposed here.
