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<p>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 <i>ℙ</i><sup>2</sup> and local <i>ℙ</i><sup>1</sup> × <i>ℙ</i><sup>1</sup>.</p>

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Resurgent Wilson loops in refined topological string

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月4日

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  • Jie Gu,
  • Gengbei Guo

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 ℙ2 and local ℙ1 × ℙ1.