We investigate the special Kahler geometry of the base of the Hitchin integrable system in terms of spectral curves and topological recursion. The Taylor expansion of the special Kahler metric about any point in the base may be computed by integrating the $g = 0$ Eynard-Orantin invariants of the corresponding spectral curve over cycles. In particular, we show that the Donagi-Markman cubic is computed by the invariant $W^{(0)}_3$. We use topological recursion to go one step beyond this and compute the symmetric quartic of second derivatives of the period matrix.

中文翻译：

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Hitchin 系统的特殊 Kähler 几何和拓扑递归

我们根据谱曲线和拓扑递归研究了 Hitchin 可积系统基础的特殊 Kahler 几何。可以通过在循环上对相应光谱曲线的 $g = 0 $ Eynard-Orantin 不变量进行积分来计算关于基中任何点的特殊 Kahler 度量的泰勒展开式。特别是，我们展示了 Donagi-Markman 三次方是由不变量 $W^{(0)}_3$ 计算的。我们使用拓扑递归更进一步，计算周期矩阵二阶导数的对称四次。