论文标题
较高的通风结构和奇异光谱曲线的拓扑递归
Higher Airy structures and topological recursion for singular spectral curves
论文作者
论文摘要
我们将基于$ W（\ Mathfrak {gl} _r）$ - 自动二级代数的量子通风结构分类的要素，基于$ \ Mathfrak的Heisenberg VOA的扭曲模块，以Weyl group $ \ mathak}的任意元素的曲折;特别是，我们构建了一类量子通风结构。我们表明，形成量子通风结构并唯一确定其分区函数的线性ODES系统等同于奇异曲线上的拓扑递归。特别是，我们的工作将Bouchard-eynard拓扑递归（有效对于平滑曲线）的定义扩展到一大类的奇异曲线，并表明不可能将其定义为其他类型的奇异性。我们还讨论了与曲线模量空间的相互关系的关系，为平滑曲线上的拓扑递归幅度提供了一般的ELSV型表示，并为在开放的$ r $ -spin交叉分裂理论中提出了精确的猜想。
We give elements towards the classification of quantum Airy structures based on the $W(\mathfrak{gl}_r)$-algebras at self-dual level based on twisted modules of the Heisenberg VOA of $\mathfrak{gl}_r$ for twists by arbitrary elements of the Weyl group $\mathfrak{S}_{r}$. In particular, we construct a large class of such quantum Airy structures. We show that the system of linear ODEs forming the quantum Airy structure and determining uniquely its partition function is equivalent to a topological recursion à la Chekhov-Eynard-Orantin on singular spectral curves. In particular, our work extends the definition of the Bouchard-Eynard topological recursion (valid for smooth curves) to a large class of singular curves, and indicates impossibilities to extend naively the definition to other types of singularities. We also discuss relations to intersection theory on moduli spaces of curves, giving a general ELSV-type representation for the topological recursion amplitudes on smooth curves, and formulate precise conjectures for application in open $r$-spin intersection theory.
