柱面上的涡旋与翘曲指数网络
Vortices on Cylinders and Warped Exponential Networks
AI总结：
该研究提出翘曲指数网络框架，计算柱面上三维N=2 U(1)陈-西蒙斯-物质理论中扭结BPS涡旋的谱，揭示其大耦合极限下的墙穿越行为，并建立稳定指标与开Gromov-Witten不变量的关联。
摘要：
我们研究柱面$C\times\mathbb{R}$上的三维$\mathcal{N}=2$ $U(1)$陈-西蒙斯-物质量子场论（QFT）。$C$的拓扑产生了被称为扭结涡旋的低能孤子BPS扇区，这些孤子在柱面两端（可能不同的）真空之间插值，同时携带磁通量。我们通过提出的**翘曲**指数网络框架，计算了孤立希格斯真空中柱面上BPS涡旋的谱。随后我们推测，这些涡旋与$\mathbb{R}^2$上的标准涡旋存在关联，而后者与环面膜的零亏格开Gromov-Witten不变量相关。更具体地说，我们证明在大Fayet-Iliopoulos耦合极限下，$C$上扭结涡旋的谱会经历无穷序列的墙穿越转变，并最终稳定。我们还提出了稳定CFIV指标的生成级数与Gromov-Witten圆盘势之间的精确关系，并讨论了其对涡旋模空间结构的影响。
英文摘要：
We study 3d $\mathcal{N}=2$ $U(1)$ Chern-Simons-matter QFT on a cylinder $C\times\mathbb{R}$. The topology of $C$ gives rise to BPS sectors of low-energy solitons known as kinky vortices, which interpolate between (possibly) different vacua at the ends of the cylinder and at the same time carry magnetic flux. We compute the spectrum of BPS vortices on the cylinder in an isolated Higgs vacuum, through the framework of \emph{warped} exponential networks, which we introduce. We then conjecture a relation between these and standard vortices on $\mathbb{R}^2$, which are related to genus-zero open Gromov-Witten invariants of toric branes. More specifically, we show that in the limit of large Fayet-Iliopoulos coupling, the spectrum of kinky vortices on $C$ undergoes an infinite sequence of wall-crossing transitions, and eventually stabilizes. We then propose an exact relation between a generating series of stabilized CFIV indices and the Gromov-Witten disk potential, and discuss its consequences for the structure of moduli spaces of vortices.
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