论文标题
n = 4个维度和非固定组的3个scfts
N = 3 SCFTs in 4 dimensions and non-simply laced groups
论文作者
论文摘要
在本文中，我们在4个维度上讨论了各种$ n = 3 $ scfts，尤其是那些可以作为分散量的分散量表获得的$ n = 4 $ symeisies的分散量。该项目的主要目的是计算库仑分支超宪法指数和希格斯分支机构希尔伯特系列系列，用于$ n = 3 $ scfts，这些系列是从衡量$ n = 4 $ super yang-yang-mills理论的全球对称组的离散子组中获得的。离散子组包含$ su（4）$ r-对称组的元素和$ n = 4 $ sym的s-二元组。此计算是针对简单的群体（其中s-二元组为$ sl（2，\ mathbb {z}）$和Bourton et al eLgebra $ l [\ mathfrak {g} $的Langlands Dual [\ Mathfrak {g}] $是Bourton等人的简单。 Arxiv：1804.05396，我们将其扩展到了非固定的群体。我们还考虑了库仑分支相对简单的情况下的库仑分支的轨道组。特别是，我们将它们与Argyres等人的结果进行了比较。 Arxiv：1904.10969，他对所有$ n \ geq 3 $ Moduli Space Orbifold几何形状分类为等级2，并取决于Bonetti等人的结果。 Arxiv：1810.03612，他为自由生成的库仑分支列出了$ n \ geq 3 $ scfts的所有可能的Orbifold组。最后，我们考虑了等级大于2并进行分析的零星复合物晶体学反射组，其中这些组可能对应于$ n = 3 $ scft。
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.
