论文标题
复杂的Chern-Simons理论在通用级别的复兴
Resurgence in complex Chern-Simons theory at generic levels
论文作者
论文摘要
在本说明中，我们研究了$ sl（2，\ mathbb {c}）$ chern-simons状态积分模型的复苏结构，补充了$ s^3 \ backslash \ mathbf {4} _1，s^3 \ s^3 \ backslash \ backslash \ mathbf {5} _2} _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 _2 $ k k k \ k \ k \ k \ \ \ \ \ \ \ \ \ \ \ \ \ \。马鞍点膨胀的系数位于整体参数扩展的结的痕迹中。尽管随着$ k $的增加，渐近系列的并发症的并发症越来越大，但渐近系列的复兴结构是普遍的：鲍勒平面奇点的分布和相关的stokes常数都与$ k $无关。
In this note we study the resurgent structure of $sl(2,\mathbb{C})$ Chern-Simons state integral models on knot complements $S^3\backslash\mathbf{4}_1,S^3\backslash\mathbf{5}_2$ with generic discrete level $k\geq 1$ and with small boundary holonomy deformation. The coefficients of the saddle point expansions are in the trace field of the knot extended by the holonomy parameter. Despite increasing complication of the asymptotic series as the level $k$ increases, the resurgent structure of the asymptotic series is universal: both the distribution of Borel plane singularities and the associated Stokes constants are independent of the level $k$.
