量子环面$\mathfrak{gl}_{1}$中超群规范理论的5d AGT对应
5d AGT correspondence of supergroup gauge theories from quantum toroidal $\mathfrak{gl}_{1}$
摘要：
讨论了A-型超群与超群规范理论的5dAGT对应。我们引入两个缠绕器，称为积极和消极的缠绕器计算的瞬子配分函数。正缠绕是普通的Awata-Feigin-Shiraishi缠绕，而负缠绕是通过使用具有负能级的中心荷获得的缠绕。我们证明了它们的合成给出了出现在超群配分函数中的基本Nekrasov因子。我们明确地导出了具有A型和D型超对称结构的超群规范理论的瞬子配分函数。利用纠缠子，我们简要地研究了Gaiotto态，$qq$ -特征标及其与代数的关系.此外，我们还证明了负缠绕子对应于Kimura和Sugimoto最近定义的反加细拓扑顶点。我们还讨论了超验理论如何出现在我们的形式主义，如果他们存在。我们在本文中研究的理论的AGT对应的存在意味着有一个更广泛的2d/4d（5d/ $q$ -代数）对应，或更一般的BPS/CFT对应，其中新的非幺正理论起着重要的作用。
英文摘要：
We discuss the 5d AGT correspondence of supergroup gauge theories with A-type supergroups. We introduce two intertwiners called positive and negative intertwiners to compute the instanton partition function. The positive intertwiner is the ordinary Awata-Feigin-Shiraishi intertwiner while the negative intertwiner is an intertwiner obtained by using central charges with negative levels. We show that composition of them gives the basic Nekrasov factors appearing in supergroup partition functions. We explicitly derive the instanton partition functions of supergroup gauge theories with A and D-type quiver structures. Using the intertwiners, we briefly study the Gaiotto state, $qq$-characters and the relation with quiver W-algebra. Furthermore, we show that the negative intertwiner corresponds to the anti-refined topological vertex recently defined by Kimura and Sugimoto. We also discuss how superquiver theories should appear in our formalism if they exist. The existence of the AGT correspondence of the theories we study in this paper implies that there is a broader 2d/4d (5d/$q$-algebra) correspondence, or more generally the BPS/CFT correspondence, where new non-unitary theories play important roles.
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