We study Hasse diagrams of moduli spaces of $\mathrm{3d}$ $\mathcal{N}=4$ quiver gauge theories. The goal of this work is twofold: 1) We introduce the notion of inverting a Hasse diagram and conjecture that the Coulomb branch and Higgs branch Hasse diagrams of certain theories are related through this operation. 2) We introduce a Hasse diagram to map out the entire moduli space of the theory, including the Coulomb, Higgs and mixed branches. For theories whose Higgs and Coulomb branch Hasse diagrams are related by inversion it is straight forward to generate the Hasse diagram of the entire moduli space. We apply inversion of the Higgs branch Hasse diagram in order to obtain the Coulomb branch Hasse diagram for bad theories and obtain results consistent with the literature. For theories whose Higgs and Coulomb branch Hasse diagrams are not related by inversion it is nevertheless possible to produce the Hasse diagram of the full moduli space using different methods. We give examples for Hasse diagrams of the entire moduli space of theories with \emph{enhanced} Coulomb branches.

中文翻译：

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3d $$ \mathcal{N} $$ = 4 颤振规范理论的哈斯图——反演和全模空间

我们研究了 $\mathrm{3d}$ $\mathcal{N}=4$ 箭袋规范理论的模空间的哈斯图。这项工作的目标是双重的：1）我们引入了反转哈斯图的概念，并推测某些理论的库仑分支和希格斯分支哈斯图通过此操作相关联。2) 我们引入了一个哈斯图来绘制理论的整个模空间，包括库仑、希格斯和混合分支。对于希格斯和库仑分支哈斯图通过反演相关的理论，可以直接生成整个模空间的哈斯图。我们应用希格斯分支哈斯图的反演，以获得不良理论的库仑分支哈斯图，并获得与文献一致的结果。对于希格斯和库仑分支哈斯图不通过反演相关的理论，仍然可以使用不同的方法产生完整模空间的哈斯图。我们给出了具有 \emph{enhanced} Coulomb 分支的理论的整个模空间的 Hasse 图的例子。