论文标题
希钦系统和n = 2个理论的家族
Families of Hitchin systems and N=2 theories
论文作者
论文摘要
通过与4D $ \ MATHCAL {N} = 2 $理论的连接的动机，我们研究了随着基础曲线在Deligne-Mummord Moduli的稳定弯曲曲线的变化时，TamelyMAMIFIED $ SL_N $ HITHINABLE SYSTEMS的全球行为。特别是，我们描述了Hitchin系统对节点基本曲线的平坦变性，并表明该节点上的可集成系统的行为部分编码在一对$（o，h）$中，其中$ o $ $ o $是nilpotent orbit，$ h $是一个简单的lie子组$ f_ {o} $ a {o} $ symemertry Groups yemmetry cop y $ o o $ o o。 Hitchin系统的家族在Deligne-Mumford Moduli空间上是非纤维化的。我们证明，Hitchin碱基融合在一起以在压实的模量空间上形成矢量束。对于$ \ overline {\ Mathcal {m}} _ {0,4} $的特定情况，我们明确地计算了此向量捆绑包。最后，我们将对任何给定的$ n $都可能出现的允许对$（o，h）$进行分类。
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 $N$.
