超共形块的超拓扑递归与Gaiotto向量
Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks
摘要：
研究了$\mathcal{N}=1$超共形块的超拓扑递归与Gaiotto向量之间的关系.具体地说，我们引入了无扭和$μ$ -扭超拓扑递归的概念，并构造了一个基于超Airy结构的对偶代数描述。然后，我们表明，一个适当的超艾里结构的配分函数与Gaiotto矢量的$\mathcal{N}=1$超共形块的Neveu-Schwarz或Ramond部门。等价地，Gaiotto向量可以通过无扭曲或$μ$扭曲的超拓扑递归来计算。这意味着超拓扑递归的框架--等价的超Airy结构--可以通过对Alday-Gaiotto-Tachikawa对应的一个拓扑扩展来计算$\mathbb{C}^2/\mathbb{Z}_2$上的$\mathcal{N}=2$纯$U(2)$超对称规范理论的Nekrasov配分函数。
英文摘要：
We investigate a relation between the super topological recursion and Gaiotto vectors for $\mathcal{N}=1$ superconformal blocks. Concretely, we introduce the notion of the untwisted and $μ$-twisted super topological recursion, and construct a dual algebraic description in terms of super Airy structures. We then show that the partition function of an appropriate super Airy structure coincides with the Gaiotto vector for $\mathcal{N}=1$ superconformal blocks in the Neveu-Schwarz or Ramond sector. Equivalently, the Gaiotto vector can be computed by the untwisted or $μ$-twisted super topological recursion. This implies that the framework of the super topological recursion -- equivalently super Airy structures -- can be applied to compute the Nekrasov partition function of $\mathcal{N}=2$ pure $U(2)$ supersymmetric gauge theory on $\mathbb{C}^2/\mathbb{Z}_2$ via a conjectural extension of the Alday-Gaiotto-Tachikawa correspondence.
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