Families of Hitchin systems and $N=2$ theories

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2020-08-03 DOI:10.4310/ATMP.2022.v26.n6.a2
A. Balasubramanian, J. Distler, R. Donagi
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引用次数: 2

Abstract

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 $N$.
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Hitchin系统族与$N=2$理论
基于与4d $\mathcal{N}=2$理论的联系,我们研究了稳定点曲线的Deligne-Mumford模空间上随底层曲线变化的可积$SL_N$ Hitchin系统族的全局行为。特别地,我们描述了Hitchin系统的平坦退化到一个节点基曲线,并证明了节点处的可积系统的行为部分编码在一对$(O,H)$中,其中$O$是一个幂零轨道,$H$是$F_{O}$的一个简单李子群,$O$是与$O$相关的一个对称群。在delign - mumford模空间上,Hitchin系统族是非平凡光纤。我们证明了一个不明显的结果,即希钦基在紧化模空间上合在一起形成一个向量束。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,我们给出了对于任意给定$N$可能出现的允许对$(O,H)$的分类。
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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