标题： 箭图聚合反应 显示英文标题

标题： Quiver Polymerisation

摘要： 两种新的图示技术应用于$3d\;\mathcal N=4$引力理论，称为链和循环引线聚合，被引入。 这些对具有多个腿的引线（或一对引线）的 Coulomb 分支全局对称性的对角$\mathrm{SU}/\mathrm{U}(k)$子群进行规范。 在 Coulomb 分支上的作用是$\mathrm{SU}/\mathrm{U}(k)$超凯勒商。 聚合技术构建并推广了来自类$\mathcal S$的已知组合方法。 聚合用于从各种物理背景生成广泛的磁引线。 这些包括 Kronheimer-Nakajima 引线的聚合构造，这些构造推广了 ADHM 构造，用于$k\;\mathrm{SU}(N)$在$\mathbb C^2$上的瞬子模空间到 A 型奇点。 还有一种来自两个$\frac{1}{2}$M5膜探测$E_6$克莱因奇点的$6d\;\mathcal N=(1,0)$的磁图的聚合构造。 我们发现了一种扩展类$\mathcal S$理论的磁图的方法，以解决在将尖点粘合到与高亏格理论相关的环路时出现的不完全希格斯化问题。 其他新颖的构造包括$\mathrm{SO}(7)$高度四的幂零轨道闭包的酉磁图。 我们探讨了在聚合过程中图的克莱布希分支和希格斯分支之间的关系。 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.