论文标题
确切的WKB和4D $ n = 2 $ pure $ su（3）$ yang-mills的Quantum seiberg-witten曲线，第一部分：abelianization
Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
论文作者
论文摘要
我们用Abelianization的语言调查了4D $ n = 2 $ n = 2 $ pure $ su（3）$ yang-mills的量子seiberg-witten曲线的确切WKB方法。相关的微分方程是$ \ mathbb {cp}^1 $的三阶方程，有两个不规则的奇异性。我们采用确切的WKB方法来研究这种三阶方程和相关的Stokes现象的解决方案。我们还研究了某个光谱问题的确切量化条件。此外，确切的WKB分析使我们考虑在平面SL的模量空间上考虑新的Darboux坐标（3，$ \ Mathbb {C} $） - 连接。特别是，在弱耦合区域中，我们遇到较高长度扭转类型的坐标，延伸Fenchel-Nielsen坐标。 Darboux坐标被认为是正式量子周期序列给出的渐近扩张。我们执行支持此猜想的数值分析。
We investigate the exact WKB method for the quantum Seiberg-Witten curve of 4d $N=2$ pure $SU(3)$ Yang-Mills, in the language of abelianization. The relevant differential equation is a third-order equation on $\mathbb{CP}^1$ with two irregular singularities. We employ the exact WKB method to study solutions to such a third-order equation and the associated Stokes phenomena. We also investigate the exact quantization condition for a certain spectral problem. Moreover, exact WKB analysis leads us to consider new Darboux coordinates on a moduli space of flat SL(3,$\mathbb{C}$)-connections. In particular, in the weak coupling region we encounter coordinates of higher length-twist type generalizing Fenchel-Nielsen coordinates. The Darboux coordinates are conjectured to admit asymptotic expansions given by the formal quantum periods series; we perform numerical analysis supporting this conjecture.
