We explore the geometrical structure of Higgs branches of quantum field theories with 8 supercharges in 3, 4, 5 and 6 dimensions. They are symplectic singularities, and as such admit a decomposition (or foliation ) into so-called symplectic leaves , which are related to each other by transverse slices . We identify this foliation with the pattern of partial Higgs mechanism of the theory and, using brane systems and recently introduced notions of magnetic quivers and quiver subtraction, we formalise the rules to obtain the Hasse diagram which encodes the structure of the foliation. While the unbroken gauge symmetry and the number of flat directions are obtainable by classical field theory analysis for Lagrangian theories, our approach allows us to characterise the geometry of the Higgs branch by a Hasse diagram with symplectic leaves and transverse slices, thus refining the analysis and extending it to non-Lagrangian theories. Most of the Hasse diagrams we obtain extend beyond the cases of nilpotent orbit closures known in the mathematics literature. The geometric analysis developed in this paper is applied to Higgs branches of several Lagrangian gauge theories, Argyres-Douglas theories, five dimensional SQCD theories at the conformal fixed point, and six dimensional SCFTs.

中文翻译：

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希格斯机制——辛奇点的哈斯图

我们探索了在 3、4、5 和 6 维上有 8 个超荷的量子场论希格斯分支的几何结构。它们是辛奇点，因此允许分解（或叶理）成所谓的辛叶，它们通过横向切片相互关联。我们用理论的部分希格斯机制模式识别这种叶理，并使用膜系统和最近引入的磁性颤动和颤动减法的概念，我们将规则形式化以获得编码叶理结构的哈斯图。而拉格朗日理论的经典场论分析可以获得完整的规范对称性和平面方向的数量，我们的方法使我们能够通过具有辛叶和横向切片的哈斯图来表征希格斯分支的几何形状，从而完善分析并将其扩展到非拉格朗日理论。我们获得的大多数哈斯图都超出了数学文献中已知的幂零轨道闭合的情况。本文中开发的几何分析应用于几种拉格朗日规范理论、阿盖尔-道格拉斯理论、共形不动点的五维 SQCD 理论和六维 SCFT 的希格斯分支。