三维$\mathcal{N}=2$ SQED $_2$和$\mathbb{CP}^1$模型中的Stokes现象
Stokes Phenomena in 3d $\mathcal{N}=2$ SQED$_2$ and $\mathbb{CP}^1$ Models
摘要：
我们提出了一种新的方法来揭示由$\mathbb{CP}^1$模型的全纯块所表现出的Stokes现象，将其视为SQED $_2$模型的一个特定的解耦极限。该方法涉及使用$\mathbb{Z}_3$对称性，该对称性使SQED $_2$模型的超对称参数空间不变，以将一对SQED $_2$全纯块变换为两对新的块。通过求解SQED $_2$模型的线算子恒等式得到的原始对和两个新的变换对被证明是由Stokes类矩阵相关的。这三对全纯嵌段可以简化为已知的三重态$\mathbb{CP}^1$嵌段，在特定的退耦极限下，SQED $_2$模型中的两个手性多重态被无限重化。然后，这种简化正确地再现了$\mathbb{CP}^1$块的斯托克斯区域和矩阵。一路上，我们发现六对SQED $_2$全纯块，这导致六个斯托克斯区域覆盖唯一的SQED $_2$模型的完整参数空间。
英文摘要：
We propose a novel approach of uncovering Stokes phenomenon exhibited by the holomorphic blocks of $\mathbb{CP}^1$ model by considering it as a specific decoupling limit of SQED$_2$ model. This approach involves using a $\mathbb{Z}_3$ symmetry that leaves the supersymmetric parameter space of SQED$_2$ model invariant to transform a pair of SQED$_2$ holomorphic blocks to get two new pairs of blocks. The original pair obtained by solving the line operator identities of the SQED$_2$ model and the two new transformed pairs turn out to be related by Stokes-like matrices. These three pairs of holomorphic blocks can be reduced to the known triplet of $\mathbb{CP}^1$ blocks in a particular decoupling limit where two of the chiral multiplets in the SQED$_2$ model are made infinitely massive. This reduction then correctly reproduces the Stokes regions and matrices of the $\mathbb{CP}^1$ blocks. Along the way, we find six pairs of SQED$_2$ holomorphic blocks in total, which lead to six Stokes-like regions covering uniquely the full parameter space of the SQED$_2$ model.
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