精细拓扑弦中的 resurgence Wilson 圈
Resurgent Wilson loops in refined topological string
AI总结：
本文研究了精细拓扑弦中Wilson圈的resurgence结构，论证了Borel奇点为积分周期且Stokes常数为精细Donaldson-Thomas不变量，通过全纯反常方程求出非微扰级数闭式解，并以local P^2和local P^1 x P^1为例验证。
摘要：
我们研究了精细拓扑弦理论中 Wilson 圈的 resurgence 结构。我们论证了 Borel 奇点应为积分周期，且相关的 Stokes 常数是精细 Donaldson-Thomas 不变量，这与自由能类似，区别仅在于 Borel 奇点不能为局部平坦坐标。我们还从精细 Wilson 圈的全纯反常方程中求解了非微扰级数的闭式解。我们以 local P^2 和 local P^1 x P^1 为例说明了这些结果。
英文摘要：
We study the resurgent structures of Wilson loops in refined topological string theory. We argue that the Borel singularities should be integral periods, and that the associated Stokes constants are refined Donaldson-Thomas invariants, just like the free energies, except that the Borel singularities cannot be local flat coordinates. We also solve the non-perturbative series in closed form from the holomorphic anomaly equations for the refined Wilson loops. We illustrate these results with the examples of local P^2 and local P^1 x P^1.
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