Reconstructing GKZ via topological recursion
Reconstructing GKZ via topological recursion
复制标题
通过拓扑递归重构GKZ
DOI：
10.1007/s00220-019-03590-6
复制
发表时间：
2019
影响因子：
2.4
通讯作者：
Ikuo Satake
中科院分区：
文献类型：
--
作者：
Hiroyuki Fuji;Kohei Iwaki;Masahide Manabe;Ikuo Satake
本文将对Gel‘fand-Kapranov-Zlevinsky系统中关于Gromov-Witten理论中Givental J函数的超几何微分方程(简称GKZ方程)提出一种新的描述。GKZ方程包含一个参数，我们将通过拓扑递推将其从经典极限重构为一条量子曲线。在这种分析中，光谱曲线(称为GKZ曲线)起着核心作用，它可以用镜像Landau-Ginzburg势的临界点集来描述。我们的新描述是通过弦理论的对偶关系得到的，各种物理解释表明，GKZ方程在上同调极限下与膜配分函数的量子曲线相同。作为GKZ方程新图解的一个应用，我们将讨论等变量模型的Stokes现象，并将检验全Stokes矩阵的跨壁公式。作为这一分析的副产品，我们将研究Dubrovin对这个等变模型的猜想。
In this article, a novel description of the hypergeometric differential equation found from Gel’fand–Kapranov–Zelevinsky’s system (referred to asGKZ equation) for Givental’sJ-function in the Gromov–Witten theory will be proposed. The GKZ equation involves a parameter, and we will reconstruct it as a quantum curve from the classical limitvia the topological recursion. In this analysis, the spectral curve (referred to asGKZ curve) plays a central role, and it can be described by the critical point set of the mirror Landau–Ginzburg potential. Our novel description is derived via the duality relations of the string theories, and various physical interpretations suggest that the GKZ equation is identified with the quantum curve for the brane partition function in the cohomological limit. As an application of our novel picture for the GKZ equation, we will discuss the Stokes phenomenon for the equivariantmodel, and the wall-crossing formula for the total Stokes matrix will be examined. And as a byproduct of this analysis, we will study Dubrovin’s conjecture for this equivariant model.