We consider compactifications of $6d$ minimal $(D_{N+3},D_{N+3})$ type conformal matter SCFTs on a generic Riemann surface. We derive the theories corresponding to three punctured spheres (trinions) with three maximal punctures, from which one can construct models corresponding to generic surfaces. The trinion models are simple quiver theories with $\mathcal{N}=1$ $SU(2)$ gauge nodes. One of the three puncture non abelian symmetries is emergent in the IR. The derivation of the trinions proceeds by analyzing RG flows between conformal matter SCFTs with different values of $N$ and relations between their subsequent reductions to $4d$. In particular, using the flows we first derive trinions with two maximal and one minimal punctures, and then we argue that collections of $N$ minimal punctures can be interpreted as a maximal one. This suggestion is checked by matching the properties of the $4d$ models such as `t Hooft anomalies, symmetries, and the structure of the conformal manifold to the expectations from $6d$. We then use the understanding that collections of minimal punctures might be equivalent to maximal ones to construct trinions with three maximal punctures, and then $4d$ theories corresponding to arbitrary surfaces, for $6d$ models described by two $M5$ branes probing a $\mathbb{Z}_k$ singularity. This entails the introduction of a novel type of maximal puncture. Again, the suggestion is checked by matching anomalies, symmetries and the conformal manifold to expectations from six dimensions. These constructions thus give us a detailed understanding of compactifications of two sequences of six dimensional SCFTs to four dimensions.

中文翻译：

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通用黎曼曲面上的 6d SCFT 序列

我们考虑在通用黎曼曲面上的 $6d$ 最小 $(D_{N+3},D_{N+3})$ 类型共形物质 SCFT 的紧化。我们推导出对应于具有三个最大穿孔的三个穿孔球体（trinions）的理论，从中可以构建对应于通用表面的模型。三元组模型是简单的颤动理论，具有 $\mathcal{N}=1$ $SU(2)$ 规范节点。三种穿刺非阿贝尔对称性之一出现在 IR 中。通过分析具有不同 $N$ 值的共形物质 SCFT 之间的 RG 流以及它们随后减少到 $4d$ 之间的关系，推导了三元组。特别是，使用流我们首先推导出具有两个最大和一个最小穿孔的三元组，然后我们认为 $N$ 最小穿孔的集合可以解释为最大穿孔。通过将 $4d$ 模型的属性（例如`t Hooft 异常、对称性和共形流形的结构）与 $6d$ 的期望进行匹配来检查该建议。然后我们使用最小穿孔的集合可能等同于最大穿孔的理解来构造具有三个最大穿孔的三元组，然后是对应于任意表面的 $4d$ 理论，对于由两个 $M5$ 膜描述的 $6d$ 模型探测 $ \mathbb{Z}_k$ 奇点。这需要引入一种新型的最大穿刺。再次，通过将异常、对称性和共形流形与来自六个维度的期望进行匹配来检查建议。因此，这些构造使我们能够详细了解两个六维 SCFT 序列到四维的紧化。