膜与克拉夫特-普罗切西转变
Branes and the Kraft-Procesi Transition
摘要：
某些3d N=4规范理论的库仑分支和希格斯分支可以理解为幂零轨道的闭包。最近，Namikawa的一个新定理表明，这是最简单的可能情况，因此给了这个类一个特殊的角色。在本说明中，我们使用膜再现卡夫和Procesi的数学工作。它研究了经典群的所有幂零轨道的分类，并通过极小奇点刻画了包含关系。我们展示了这些最小的奇点是如何自然产生的IIB型超弦嵌入的3D A型理论。希格斯机制可以用来消除最小奇异性，对应于膜配置的转变，诱导一个新的有效的3d理论。这再现了Kraft-Procesi的结果，赋予了规范理论家族一个新的基本结构。我们提供了一个有效的程序来计算这样的膜过渡。
英文摘要：
The Coulomb and Higgs branches of certain 3d N=4 gauge theories can be understood as closures of nilpotent orbits. Recently, a new theorem by Namikawa suggests that this is the simplest possible case, thus giving this class a special role. In this note we use branes to reproduce the mathematical work by Kraft and Procesi. It studies the classification of all nilpotent orbits for classical groups and it characterizes an inclusion relation via minimal singularities. We show how these minimal singularities arise naturally in the Type IIB superstring embedding of the 3d A-type theories. The Higgs mechanism can be used to remove the minimal singularity, corresponding to a transition in the brane configuration that induces a new effective 3d theory. This reproduces the Kraft-Procesi results, endowing the family of gauge theories with a new underlying structure. We provide an efficient procedure for computing such brane transitions.
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