论文标题
SU的复发分析（2）Chern-Simons分区功能在Brieskorn Spheres $σ（2,3,6n+5）$
Resurgent Analysis of SU(2) Chern-Simons Partition Function on Brieskorn Spheres $Σ(2,3,6n+5)$
论文作者
论文摘要
$ \ hat {z} $ - 可以重建SU（2）Chern-Simons分区的分析延续，通过Borel重新召开，被GPV发现，并已猜想是将3-元人的新同源物降低，可以将3d $ n $ 3d $ 3D;由GPPV。特别是，$ \ hat {z} $的复兴分析在发现WRT不变性的分析属性方面富有成果。对于$σ（2,3,5）的案例，对这些$ \ hat {z} $ - 不变的分析，GMP的$σ（2,3,5），\σ（2,3,7）$，Chun $σ（2,5,7）$由Chung和Kucharski，Indectionally，Chun和其他一些塞弗特词。在本文中，我们将$ \ hat {z} $的复兴分析扩展到一个Brieskorn同源性的家族$σ（2,3,6n+5）$中，其中$ n \ in \ Mathbb {z} _+$和$ 6n+5 $是PRIME。根据GPPV和Hikami，通过$σ（2,3,6n+5）$得出$ \ hat {z} $，我们提供了一个公式，可以在其中快速计算SU（2）Chern-Simons分区功能的完全分析延续的非扰动贡献。
$\hat{Z}$-invariants, which can reconstruct the analytic continuation of the SU(2) Chern-Simons partition functions via Borel resummation, were discovered by GPV and have been conjectured to be a new homological invariant of 3-manifolds which can shed light onto the superconformal and topologically twisted index of 3d $\mathcal{N}=2$ theories proposed by GPPV. In particular, the resurgent analysis of $\hat{Z}$ has been fruitful in discovering analytic properties of the WRT invariants. The resurgent analysis of these $\hat{Z}$-invariants has been performed for the cases of $Σ(2,3,5),\ Σ(2,3,7)$ by GMP, $Σ(2,5,7)$ by Chun, and, more recently, some additional Seifert manifolds by Chung and Kucharski, independently. In this paper, we extend and generalize the resurgent analysis of $\hat{Z}$ on a family of Brieskorn homology spheres $Σ(2,3,6n+5)$ where $n\in\mathbb{Z}_+$ and $6n+5$ is a prime. By deriving $\hat{Z}$ for $Σ(2,3,6n+5)$ according to GPPV and Hikami, we provide a formula where one can quickly compute the non-perturbative contributions to the full analytic continuation of SU(2) Chern-Simons partition function.
