$E_6$理论的修补玩具
Tinkertoys for the $E_6$ Theory
摘要：
在Riemann曲面$C$上紧化ADE类型的6维（2，0）超共形场论，在$C$上的点处使用余维2缺陷算子，产生4维$\mathcal{N}=2$超共形场论。一个突出的问题是，以这种方式对人们获得的4D理论进行分类，并理解它们的性质。在本文中，我们将注意力转向$E_6$（2，0）理论，它（与A-和D-级数不同）没有用M5-膜实现。对4D理论进行分类相当于对所有的3穿孔球体（“固定装置”）以及连接它们的圆柱体进行分类，这可能发生在$C$的裤子分解中。我们找到904 fixtures：19个对应于自由超多重态，825个对应于孤立的相互作用SCFT（没有已知的拉格朗日描述），60个“混合固定装置”对应于自由超多重态和相互作用SCFT的组合。在825个相互作用的装置中，我们只列出了139个“有趣”的装置。作为应用，我们研究了拉格朗日场论的强耦合极限：在$27$中有4个超多重态的$E_6$和在$26$中有3个超多重态的$F_4$.
英文摘要：
Compactifying the 6-dimensional (2,0) superconformal field theory, of type ADE, on a Riemann surface, $C$, with codimension-2 defect operators at points on $C$, yields a 4-dimensional $\mathcal{N}=2$ superconformal field theory. An outstanding problem is to classify the 4D theories one obtains, in this way, and to understand their properties. In this paper, we turn our attention to the $E_6$ (2,0) theory, which (unlike the A- and D-series) has no realization in terms of M5-branes. Classifying the 4D theories amounts to classifying all of the 3-punctured spheres ("fixtures"), and the cylinders that connect them, that can occur in a pants-decomposition of $C$. We find 904 fixtures: 19 corresponding to free hypermultiplets, 825 corresponding to isolated interacting SCFTs (with no known Lagrangian description) and 60 "mixed fixtures", corresponding to a combination of free hypermultiplets and an interacting SCFT. Of the 825 interacting fixtures, we list only the 139 "interesting" ones. As an application, we study the strong coupling limits of the Lagrangian field theories: $E_6$ with 4 hypermultiplets in the $27$ and $F_4$ with 3 hypermultiplets in the $26$.
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