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arXiv 2004.03919hep-th
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N = 3个4维和非简单编织组的SCFT

N = 3 SCFTs in 4 dimensions and non-simply laced groups

Mikhail Evtikhiev

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12 pages
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摘要：

在本文中，我们讨论了各种$N=3$ SCFT在4维，特别是那些可以获得作为一个离散规范的$N=4$ SYM理论与非简单的花边集团。该项目的主要目标是计算$N=3$ SCFT的库仑分支超共形指数和希格斯分支希尔伯特级数，这些SCFT是通过测量$N=4$超级杨-米尔斯理论的全局对称群的离散子群而获得的。离散子群包含$SU(4)$ R-对称群和$N=4$ SYM的S-对偶群的元素。Bourton等人在arXiv：1804.05396中对单缀群（其中S-对偶群是$SL(2, \mathbb{Z})$，代数$L[\mathfrak{g}]$的Langlands对偶是简单的$\mathfrak{g}$）进行了这种计算，我们将其推广到非单缀群。我们还考虑了库仑分支相对简单时库仑分支的轨道折叠群;特别地，我们将它们与Argyres等人的结果进行了比较。arXiv：1904.10969，他们将所有$N\geq 3$模空间轨道折叠几何分类为秩2，并与Bonetti等人的结果进行了比较。arXiv：1810.03612，他们列出了$N\geq 3$ SCFT自由生成的库仑分支的所有可能的轨道折叠群。最后，我们考虑了秩大于2的零星复杂晶体反射群并进行了分析，其中哪些可以对应于$N=3$ SCFT。

英文摘要：

In this paper we discuss various $N=3$ SCFTs in 4 dimensions and in particular those which can be obtained as a discrete gauging of an $N=4$ SYM theories with non-simply laced groups. The main goal of the project was to compute the Coulomb branch superconformal index and Higgs branch Hilbert series for the $N=3$ SCFTs that are obtained from gauging a discrete subgroup of the global symmetry group of $N=4$ Super Yang-Mills theory. The discrete subgroup contains elements of both $SU(4)$ R-symmetry group and the S-duality group of $N=4$ SYM. This computation was done for the simply laced groups (where the S-duality groups is $SL(2, \mathbb{Z})$ and Langlands dual of the the algebra $L[\mathfrak{g}]$ is simply $\mathfrak{g}$) by Bourton et al. arXiv:1804.05396, and we extended it to the non-simply laced groups. We also considered the orbifolding groups of the Coulomb branch for the cases when Coulomb branch is relatively simple; in particular, we compared them with the results of Argyres et al. arXiv:1904.10969, who classified all $N\geq 3$ moduli space orbifold geometries at rank 2 and with the results of Bonetti et al. arXiv:1810.03612, who listed all possible orbifolding groups for the freely generated Coulomb branches of $N\geq 3$ SCFTs. Finally, we have considered sporadic complex crystallographic reflection groups with rank greater than 2 and analyzed, which of them can correspond to an $N=3$ SCFT.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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