论文标题
解决方案的量子Riemann-Hilbert问题
Quantum Riemann-Hilbert problems for the resolved conifold
论文作者
论文摘要
我们研究了由精制的Donaldson-Thomas理论确定的量子Riemann-Hilbert问题。使用贝德格兰（Beidgeland）对经典的黎曼 - 希尔伯特（Riemann-Hilbert）问题的解决方案，我们根据具有不平等参数的多个正弦函数提供了明确的解决方案。解决方案的新功能是量子参数的有效区域$ q^{\ frac {1} {2}}} = \ exp（πiτ）$随稳定条件和bps $ t $平面而变化。将解决方案与精致的Chern-Simons理论的分区函数进行比较，并调用大$ n $ string二元性，我们发现该解决方案包含在分辨率化的Conifold上的精制拓扑字符串的非扰动完成。因此，解决量子Riemann-Hilbert问题为Donaldson-Thomas理论提供了可能的非扰动定义。
We study the quantum Riemann-Hilbert problems determined by the refined Donaldson-Thomas theory on the resolved conifold. Using the solutions to classical Riemann-Hilbert problems by Beidgeland, we give explicit solutions in terms of multiple sine functions with unequal parameters. The new feature of the solutions is that the valid region of the quantum parameter $q^{\frac{1}{2}}=\exp(πi τ)$ varies on the space of stability conditions and BPS $t$-plane. Comparing the solutions with the partition function of refined Chern-Simons theory and invoking large $N$ string duality, we find that the solution contains the non-perturbative completion of the refined topological string on the resolved conifold. Therefore solving the quantum Riemann-Hilbert problems provides a possible non-perturbative definition for the Donaldson-Thomas theory.
