Towards a classification of rank r $$ \mathcal{N} $$ = 2 SCFTs. Part II. Special Kahler stratification of the Coulomb branch
Towards a classification of rank r $$ \mathcal{N} $$ = 2 SCFTs. Part II. Special Kahler stratification of the Coulomb branch
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DOI：
10.1007/jhep12(2020)022
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发表时间：
2020-06
影响因子：
5.4
通讯作者：
P. Argyres;M. Martone
中科院分区：
文献类型：
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作者：
P. Argyres;M. Martone
我们研究四维 = 2 库仑分支的奇异轨迹的分层。我们在此分层上提出了一组自洽条件，可用于将尺度不变的 1 阶库仑分支几何形状的分类扩展到两个复杂的维度，甚至更高。这里提出的论点的计算简单性源于这样一个事实：所需的主要成分 - 1 级变形模式和 2 级地层的夹杂物模式 - 是离散拓扑数据，通过它们与 SCFT 中心电荷的关系满足强自洽条件。这里使用了分层数据与中心电荷的这种关系，但它是由一位作者在另一篇配套论文中推导和解释的。我们通过重新分析许多先前已知的 2 阶 SCFT 示例以及查找新理论的示例来说明这些条件的使用。这些条件的力量源于这样一个事实：对于库仑分支分层，物理上允许的“基本切片”的推测完整列表是已知的。相比之下，限制与希格斯分支分层相关的辛奇点的可能基本切片仍然是一个悬而未决的问题。
We study the stratification of the singular locus of four dimensional= 2 Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant rank 1 Coulomb branch geometries to two complex dimensions, and beyond. The calculational simplicity of the arguments presented here stems from the fact that the main ingredients needed - the rank 1 deformation patterns and the pattern of inclusions of rank 2 strata - are discrete topological data which satisfy strong self-consistency conditions through their relationship to the central charges of the SCFT. This relationship of the stratification data to the central charges is used here, but is derived and explained in a companion paper by one of the authors. We illustrate the use of these conditions by re-analyzing many previously-known examples of rank 2 SCFTs, and also by finding examples of new theories. The power of these conditions stems from the fact that for Coulomb branch stratifications a conjecturally complete list of physically allowed “elementary slices” is known. By contrast, constraining the possible elementary slices of symplectic singularities relevant for Higgs branch stratifications remains an open problem.