标题： 箭图聚合 显示英文标题

标题： Quiver Polymerisation

摘要： 介绍两种关于$3d\;\mathcal N=4$轨形规范理论的新图技术，称为链式和循环轨形聚合。 这些技术通过多个分支的轨形（或一对轨形）的 Coulomb 支路全局对称性的对角$\mathrm{SU}/\mathrm{U}(k)$子群来规范作用。 在 Coulomb 支路上的作用是一个$\mathrm{SU}/\mathrm{U}(k)$超 Kähler 商。 聚合技术从$\mathcal S$类构建并推广了已知的合成方法。 聚合被用来从各种物理背景生成广泛的磁轨形。 其中包括 Kronheimer-Nakajima 轨形的聚合构造，它将 ADHM 构造推广到$k\;\mathrm{SU}(N)$在$\mathbb C^2$上的瞬子模空间到 A 型奇点上。 同样地，对于由两个$\frac{1}{2}$M5 膜探测$E_6$Klein 奇点而得到的$6d\;\mathcal N=(1,0)$的磁性箭图，我们也构建了一个聚合过程。 我们找到了一种扩展 Class$\mathcal S$理论磁性箭图的方法，以解决在将裂隙粘接到与高亏格理论相关的环路时出现的不完全Higgs化问题。 其他新颖的构造包括一个用于$\mathrm{SO}(7)$高度为四的幂零轨道闭包的酉磁性箭图。 我们探讨了在聚合过程中磁性箭图的Coulomb分支和Higgs分支之间的关系。 显示英文摘要

摘要： Two new diagrammatic techniques on $3d\;\mathcal N=4$ quiver gauge theories, termed chain and cyclic quiver polymerisation are introduced. These gauge a diagonal $\mathrm{SU}/\mathrm{U}(k)$ subgroup of the Coulomb branch global symmetry of a quiver (or pair of quivers) with multiple legs. The action on the Coulomb branch is that of a $\mathrm{SU}/\mathrm{U}(k)$ hyper-K\"ahler quotient. The polymerisation techniques build and generalise known composition methods from class $\mathcal S$. Polymerisation is used to generate a wide range of magnetic quivers from various physical contexts. These include polymerisation constructions for Kronheimer-Nakajima quivers, which generalise the ADHM construction for the moduli space of $k\;\mathrm{SU}(N)$ instantons on $\mathbb C^2$ to A-type singularities. Also a polymerisation construction of the magnetic quiver for the $6d\;\mathcal N=(1,0)$ coming from two $\frac{1}{2}$ M5 branes probing an $E_6$ Klein singularity. We find a method of extending magnetic quivers for Class $\mathcal S$ theories to cure the incomplete Higgsing that arises when gluing punctures into the loops associated with higher genus theories. Other novel constructions include a unitary magnetic quiver for the closure of a height four nilpotent orbit of $\mathrm{SO}(7)$. We explore the relationships between the Coulomb and Higgs branches of quivers under polymerisation.