论文标题
量子圆环$ \ mathfrak {gl} _ {1} $的5D AGT通信超组理论
5d AGT correspondence of supergroup gauge theories from quantum toroidal $\mathfrak{gl}_{1}$
论文作者
论文摘要
我们讨论了使用A型超组的超组理论的5D AGT对应关系。我们介绍了两个称为正和负互穿的互换者来计算激体顿分区函数。正跨区域是普通的AWATA-FEIGIN-SHIRAISHI互相区，而负透明机是通过使用负级别的中央电荷获得的互相区域。我们表明，它们的组成给出了超组分区功能中出现的基本Nekrasov因素。我们明确地推导了具有A和D型Quiver结构的超组理论的instanton分区函数。使用Intertwiners，我们简要研究了Gaiotto州，$ QQ $ - 字符以及与Quiver W-Algebra的关系。此外，我们表明，负互穿的对应于Kimura和Sugimoto最近定义的反精制拓扑顶点。我们还讨论了超级Quiver理论是否存在在我们的形式主义中应该如何出现。我们在本文中研究的理论的AGT对应关系的存在意味着，有更广泛的2D/4D（5D/$ Q $ -Algebra）对应关系，或更一般而言的BPS/CFT对应关系，其中新的非独立理论起着重要的作用。
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.
