D n Dynkin quiver moduli spaces
D n Dynkin quiver moduli spaces
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DOI：
10.1088/1751-8121/ab4344
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发表时间：
2019-02
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通讯作者：
Jamie Rogers;R. Tǎtar
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文献类型：
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作者：
Jamie Rogers;R. Tǎtar
我们研究了3d $ $\mathcal{N}=4$N规范理论，其规范节点形成了一个$D_n$ Dynkin图.这类良好的$D_n$ Dynkin箭图是完全特征和模空间奇异性结构完全确定的所有这样的理论。好的$D_n$ Dynkin箭图的类记为$D_\nu^\mu（n）_p$，其中$n \geq 2$是整数，$\nu$和$\mu$是整数分割，$p \in \{ \textrm{even}，\textrm{odd}\}$表示两个广泛子类之一的成员。一个完整的评估$\mathfrak{so}_{2n}$幂零品种是可实现的$D_n$ Dynkin的模空间。引入箭图加法，并利用箭图加法给出了$D_n$ Dynkin箭图偏序集结构的大子类.模空间分支的包含关系决定了它们的偏序。所得的Hasse图被用来分类$D_n$ Dynkin箭图和确定任意好理论的模空间奇异结构。偏序集的建设和局部模空间分析的补充，整个明确的检查，利用模空间尺寸匹配。
We study $3d$ $\mathcal{N}=4$ quiver gauge theories with gauge nodes forming a $D_n$ Dynkin diagram. The class of good $D_n$ Dynkin quivers is completely characterised and the moduli space singularity structure fully determined for all such theories. The class of good $D_n$ Dynkin quivers is denoted $D_\nu^\mu(n)_p$ where $n \geq 2$ is an integer, $\nu$ and $\mu$ are integer partitions and $p \in \{ \textrm{even}, \textrm{odd}\}$ denotes membership of one of two broad subclasses. A full assessment of which $\mathfrak{so}_{2n}$ nilpotent varieties are realisable as $D_n$ Dynkin quiver moduli spaces is provided. Quiver addition is introduced and is used to give large subclasses of $D_n$ Dynkin quivers poset structure. The partial ordering is determined by inclusion relations for the moduli space branches. The resulting Hasse diagrams are used to both classify $D_n$ Dynkin quivers and determine the moduli space singularity structure for an arbitrary good theory. The poset constructions and local moduli space analyses are complemented throughout by explicit checks utilising moduli space dimension matching.