小$E_8$ Instanton和Kraft Process过渡
The Small $E_8$ Instanton and the Kraft Procesi Transition
摘要：
六维空间中最简单的$(1,0)$超对称理论之一，存在于一个M5膜在$(1,0)$型奇点$\mathbb{C}^2/D_k$处的世界体积上。低能理论是由SQCD理论给出的，该理论具有$Sp(k-4)$规范群，精确的无反常$2k$味数，以及由逆规范耦合设定的标度。有限耦合$\mathcal{H}_f$的希格斯分支是$D_{2k}$的幂零轨道的闭合，并且随着逆规范耦合被设置为零，发展出更多的平坦方向（违反了错误地声称希格斯分支仍然是经典的标准知识）。对于任何$k$，四元数维度都增加了$29$，希格斯分支不再是$k>4$的幂零轨道的闭合，除了$k=4$，它变成了$\overline{{\rm min}_{E_8}}$，$E_8$的最小幂零轨道的闭合，因此在六维中具有罕见的味道对称性增强现象。在几何上，$\mathcal{H}_f \subset \mathcal{H}_{\infty}$的自然包含符合Brieskorn Slodowy的横向切片理论，并且对于任何$k>3$，横向切片被计算为$\overline{{\rm min}_{E_8}}$。这与众所周知的小$E_8$瞬子跃迁相一致，其中1个张量多重态与29个超多重态交换，从而给出了几何理论的物理解释。通过与经典情况的类比，我们称之为卡夫过程转变。
英文摘要：
One of the simplest $(1,0)$ supersymmetric theories in six dimensions lives on the world volume of one M5 brane at a $D$ type singularity $\mathbb{C}^2/D_k$. The low energy theory is given by an SQCD theory with $Sp(k-4)$ gauge group, a precise number of $2k$ flavors which is anomaly free, and a scale which is set by the inverse gauge coupling. The Higgs branch at finite coupling $\mathcal{H}_f$ is a closure of a nilpotent orbit of $D_{2k}$ and develops many more flat directions as the inverse gauge coupling is set to zero (violating a standard lore that wrongly claims the Higgs branch remains classical). The quaternionic dimension grows by $29$ for any $k$ and the Higgs branch stops being a closure of a nilpotent orbit for $k>4$, with an exception of $k=4$ where it becomes $\overline{{\rm min}_{E_8}}$, the closure of the minimal nilpotent orbit of $E_8$, thus having a rare phenomenon of flavor symmetry enhancement in six dimensions. Geometrically, the natural inclusion of $\mathcal{H}_f \subset \mathcal{H}_{\infty}$ fits into the Brieskorn Slodowy theory of transverse slices, and the transverse slice is computed to be $\overline{{\rm min}_{E_8}}$ for any $k>3$. This is identified with the well known small $E_8$ instanton transition where 1 tensor multiplet is traded with 29 hypermultiplets, thus giving a physical interpretation to the geometric theory. By the analogy with the classical case, we call this the Kraft Procesi transition.
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