扭曲的 $A_{2N}$ Argyres--Douglas 理论：顶点代数、Higgs 分支与二重覆盖
Twisted $A_{2N}$ Argyres--Douglas theories: vertex algebras, Higgs branches, and double covers
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- University of Oxford（牛津大学）
- Institute for Advanced Study（普林斯顿高等研究院）
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中文总结 AI 辅助
研究扭曲A_{2N}与D_{N+1}系列广义Argyres-Douglas理论，提出A系列为D系列的幂零Higgsing，其顶点代数为容许水平仿射Kac-Moody代数的有限扩张，Higgs分支多为幂零轨道闭包的二重覆盖，并给出幺正SCFT例子。
中文摘要 AI 辅助
我们研究了广义 Argyres--Douglas 理论的两个密切相关族的相关顶点算子代数和 Higgs 分支，这两个族分别源于扭曲的 $A_{2N}$ 系列和扭曲的 $D_{N+1}$ 系列。我们提出 $A$ 系列理论可实现为 $D$ 系列的幂零 Higgsing，并为此提议汇集了多种证据。一个推论是，$A$ 系列的相关顶点算子代数是仿射 Kac--Moody 顶点代数在（非边界）容许水平下的有限扩张，而非这些 Kac--Moody 代数本身，并且它们的 Higgs 分支在许多情况下是幂零轨道闭包的二重覆盖。$A$ 系列理论的 $\mathbb{Z}_2$ 规范化为幺正 SCFT 提供了例子，其相关顶点算子代数恰好是非边界容许水平下的仿射 Kac--Moody 代数。我们提出这些顶点代数配备了一个非标准的 $\mathfrak{R}$-滤过，并评论了与分级幺正性的相容性。
英文摘要
We investigate the associated vertex operator algebras and Higgs branches of two closely related families of generalised Argyres--Douglas theories, arising from the twisted $A_{2N}$ and twisted $D_{N+1}$ series, respectively. We propose that the $A$-series theories are realised as nilpotent Higgsings of the $D$-series, and we assemble a variety of pieces of evidence for this proposal. A consequence is that the associated vertex operator algebras of the $A$-series are finite extensions of affine Kac--Moody vertex algebras at (non-boundary) admissible levels, rather than those Kac--Moody algebras themselves, and that their Higgs branches are in many cases double covers of nilpotent orbit closures. The $\mathbb{Z}_2$ gaugings of the $A$-series theories then furnish examples of unitary SCFTs whose associated vertex operator algebras are precisely affine Kac--Moody algebras at non-boundary admissible levels. We propose that these vertex algebras are equipped with a non-standard $\mathfrak{R}$-filtration, and comment on compatibility with graded unitarity.
