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arXiv 2211.01403hep-thmath-phmath.MP
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拓扑弦理论中的精确多瞬子

Exact multi-instantons in topological string theory

Jie Gu, Marcos Marino

AI总结:

本文在局部Calabi-Yau流形上求解BCOV全纯异常方程的trans-series扩展,得到多瞬子振幅的精确闭式解,揭示其与矩阵模型隧穿振幅的相似性及平坦坐标的量子化结构,并给出局部拓扑弦的复活结构图像。

摘要:

拓扑弦理论具有多瞬子扇区,这些扇区导致弦耦合常数中的非微扰效应,并控制微扰亏格展开的大阶行为。正如Couso、Edelstein、Schiappa和Vonk所提出的,这些扇区可以通过BCOV全纯异常方程的trans-series扩展来描述。在本文中,我们在局部Calabi-Yau流形的情形下找到了这些多瞬子trans-series的精确闭式解。所得到的多瞬子振幅结果与矩阵模型的特征值隧穿振幅非常相似。它们的形式表明,Calabi-Yau流形的平坦坐标自然地以弦耦合常数为单位进行量子化,正如大$N$对偶性中所假设的那样。基于我们的结果,我们获得了局部情形下拓扑弦的复活结构的一般图像,并以局部$\mathbb{P}^2$情形下的显式计算加以说明。

英文摘要:

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 $\mathbb{P}^2$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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