We study the Riemann-Hilbert problems of [6] (T. Bridgeland, “Riemann-Hilbert problems from Donaldson–Thomas theory”, arxiv:1611.03697) in the case of the Donaldson–Thomas theory of the resolved conifold. We give explicit solutions in terms of the Barnes double and triple sine functions. We show that the $\tau$-function of [6] is a non-perturbative partition function, in the sense that its asymptotic expansion coincides with the topological closed string partition function.

中文翻译：

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解析的凸函数和非扰动分区函数的Riemann-Hilbert问题

我们以解析子集的唐纳森-托马斯理论为例研究[6]的黎曼-希尔伯特问题（T. Bridgeland，“来自唐纳森-托马斯理论的黎曼-希尔伯特问题”，arxiv：1611.03697）。我们根据Barnes双正弦函数和三正弦函数给出明确的解决方案。从[6]的$ \ tau $函数可以看出，它的渐近扩展与拓扑闭合字符串分区函数一致，这是一个非扰动分区函数。