For a complex simple simply connected Lie group $G$, and a compact Riemann surface $C$, we consider two sorts of families of flat $G$-connections over $C$. Each family is determined by a point $\mathbf{u}$ of the base of Hitchin’s integrable system for $(G,C)$. One family $\nabla_{\hbar ,\mathbf{u}}$ consists of $G$-opers, and depends on $\hbar \in \mathbb{C}^\times$. The other family $\nabla_{R, \zeta,\mathbf{u}}$ is built from solutions of Hitchin’s equations, and depends on $\zeta \in \mathbb{C}^\times , R \in \mathbb{R}^+$. We show that in the scaling limit $R \to 0, \zeta = \hbar R$, we have $\nabla_{R,\zeta,\mathbf{u}} \to \nabla_{\hbar,\mathbf{u}}$. This establishes and generalizes a conjecture formulated by Gaiotto.

中文翻译：

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从希钦（Hitchin）地区到诺贝丽·霍奇（Nonabelian Hodge）的歌剧院

对于一个复杂的简单连接的李群$ G $和一个紧凑的Riemann曲面$ C $，我们考虑了两种类型的平面$ G $连接-$ C $以上的连接。每个家庭都由Hitchin可积系统的$（G，C）$的点$ \ mathbf {u} $来确定。一个家庭$ \ nabla _ {\ hbar，\ mathbf {u}} $由$ G $ -opers组成，并且取决于$ \ hbar \ in \ mathbb {C} ^ \ times $。另一个家庭$ \ nabla_ {R，\ zeta，\ mathbf {u}} $是根据Hitchin方程的解建立的，并且取决于$ \ zeta \ in \ mathbb {C} ^ \ times，R \ in \ mathbb { R} ^ + $。我们显示出在缩放限制$ R \到0，\ zeta = \ hbar R $，我们有$ \ nabla_ {R，\ zeta，\ mathbf {u}} \ to \ nabla _ {\ hbar，\ mathbf {u }} $。这建立并概括了Gaiotto提出的猜想。