论文标题
量子结的复发结构不变性
The resurgent structure of quantum knot invariants
论文作者
论文摘要
复杂的Chern-Simons理论中量子结的渐近膨胀导致了分歧的形式功率序列。我们猜想这些系列是复兴的功能，其stokes自动形态由一对具有整数系数的$ q $ series矩阵给出，这些矩阵由一对线性$ q $ difference方程的基本解决方案明确确定。我们进一步猜测，对于双曲线结，这些矩阵的出色进入等于Dimofte-Gaiotto-Gukov 3D索引，因此由BPS状态的计数给出。我们通过在$ 4_1 $和$ 5_2 $节的情况下与理论和数字计算的整数匹配来明确说明我们的猜想。
The asymptotic expansion of quantum knot invariants in complex Chern-Simons theory gives rise to factorially divergent formal power series. We conjecture that these series are resurgent functions whose Stokes automorphism is given by a pair of matrices of $q$-series with integer coefficients, which are determined explicitly by the fundamental solutions of a pair of linear $q$-difference equations. We further conjecture that for a hyperbolic knot, a distinguished entry of those matrices equals to the Dimofte-Gaiotto-Gukov 3D-index, and thus is given by a counting of BPS states. We illustrate our conjectures explicitly by matching theoretically and numerically computed integers for the cases of the $4_1$ and the $5_2$ knots.
