论文标题
关于量子周期的复发结构
On the resurgent structure of quantum periods
论文作者
论文摘要
量子周期出现在许多情况下，从量子力学到局部镜像对称性。可以在所谓的Nekrasov-Shatashvili限制中用拓扑弦的自由能和威尔逊循环来描述它们。我们考虑了这些数量满足的全体形态异常方程的跨系列扩展，并为这些跨系列获得了精确的多in-Instanton溶液。在此结果的基础上，我们提出了统一的观点，以了解量子周期的复兴结构。例如，我们表明，最初在量子机械示例中获得的Delabaere-Pham公式是量子周期的一般特征。我们通过对量子力学的双孔的明确计算以及本地$ \ mathbb {p}^2 $的量子镜曲线来说明我们的一般结果。
Quantum periods appear in many contexts, from quantum mechanics to local mirror symmetry. They can be described in terms of topological string free energies and Wilson loops, in the so-called Nekrasov-Shatashvili limit. We consider the trans-series extension of the holomorphic anomaly equations satisfied by these quantities, and we obtain exact multi-instanton solutions for these trans-series. Building on this result, we propose a unified perspective on the resurgent structure of quantum periods. We show for example that the Delabaere-Pham formula, which was originally obtained in quantum mechanical examples, is a generic feature of quantum periods. We illustrate our general results with explicit calculations for the double-well in quantum mechanics, and for the quantum mirror curve of local $\mathbb{P}^2$.
