Motivated by the connection to 4d $\mathcal{N} = 2$ theories, we study the global behavior of families of tamely-ramified $SL_N$ Hitchin integrable systems as the underlying curve varies over the Deligne–Mumford moduli space of stable pointed curves. In particular, we describe a flat degeneration of the Hitchin system to a nodal base curve and show that the behaviour of the integrable system at the node is partially encoded in a pair $(O,H)$ where $O$ is a nilpotent orbit and $H$ is a simple Lie subgroup of $F_O$, the flavour symmetry group associated to $O$. The family of Hitchin systems is nontrivially-fibered over the Deligne–Mumford moduli space. We prove a non-obvious result that the Hitchin bases fit together to form a vector bundle over the compactified moduli space. For the particular case of $\overline{\mathcal{M}}_{0,4}$, we compute this vector bundle explicitly. Finally, we give a classification of the allowed pairs $(O,H)$ that can arise for any given $N$.

中文翻译：

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希钦系统家族和 $N=2$ 理论

受与 4d $\mathcal{N} = 2$ 理论联系的启发，我们研究了随着基础曲线在稳定尖曲线的 Deligne-Mumford 模空间上变化，驯服分支 $SL_N$ 希钦可积系统族的全局行为。特别是，我们将希钦系统的平坦退化描述为节点基曲线，并表明可积系统在节点处的行为部分编码在一对 $(O,H)$ 中，其中 $O$ 是幂零轨道$H$ 是 $F_O$ 的简单李子群，$F_O$ 是与 $O$ 相关的风味对称群。希钦系统家族在德利涅-芒福德模空间上具有非平凡的纤维化特征。我们证明了一个不明显的结果，即希钦基组合在一起形成紧致模空间上的向量丛。对于 $\overline{\mathcal{M}}_{0,4}$ 的特殊情况，我们显式地计算这个向量束。最后，我们给出对于任何给定的 $N$ 可能出现的允许对 $(O,H)$ 的分类。