论文标题
拓扑弦理论中的确切多数互联
Exact multi-instantons in topological string theory
论文作者
论文摘要
拓扑字符串理论具有多个互联网扇区，可导致弦耦合常数的非扰动效应，并控制扰动属膨胀的大阶行为。正如Couso，Edelstein，Schiappa和Vonk所提出的那样，这些部门可以通过BCOV Holomorphic异常方程的跨系列扩展来描述。在本文中，我们在局部卡拉比（Calabi-Yau）歧管的情况下找到了这些多个内斯坦跨系列的精确封闭形式的解决方案。结果，所得的多in-Instanton振幅与矩阵模型的特征值隧道振幅非常相似。它们的形式表明，如大型$ n $二元性所述，卡拉比远流形的平坦坐标是自然量化的。基于我们的结果，我们在本地情况下获得了拓扑字符串复发结构的一般图片，在本地$ \ mathbb {p}^2 $的情况下，我们用显式计算说明了这一点。
Topological string theory has multi-instanton sectors which lead to non-perturbative effects in the string coupling constant and control the large order behavior of the perturbative genus expansion. As proposed by Couso, Edelstein, Schiappa and Vonk, these sectors can be described by a trans-series extension of the BCOV holomorphic anomaly equations. In this paper we find exact, closed form solutions for these multi-instanton trans-series in the case of local Calabi-Yau manifolds. The resulting multi-instanton amplitudes turn out to be very similar to the eigenvalue tunneling amplitudes of matrix models. Their form suggests that the flat coordinates of the Calabi-Yau manifold are naturally quantized in units of the string coupling constant, as postulated in large $N$ dualities. Based on our results we obtain a general picture for the resurgent structure of the topological string in the local case, which we illustrate with explicit calculations in the case of local $\mathbb{P}^2$.
