阿贝尔希格斯模型中的稳定解
Stable solutions in the abelian Higgs model
- ETH Zürich（苏黎世联邦理工学院）
- Bocconi University（博科尼大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文分类了4维阿贝尔希格斯模型中二次能量增长的稳定解，证明其全纯性并满足Bradlow方程，节点集为全纯曲线，并构造了任意指定节点集的解，推论得到三维线性能量增长稳定解为二维Bogomolnyi涡旋。
AI中文摘要：
我们分类了在4维阿贝尔希格斯模型中具有二次能量增长的完整稳定解。更精确地，我们证明了这样的解相对于某个复结构是全纯的，即它们满足Bradlow引入的一阶方程，因此它们的节点集是全纯曲线。反之，我们构造了节点集为任意具有二次面积增长的给定全纯曲线的解。作为推论，我们证明了在$\mathbb{R}^3$中所有具有线性能量增长的稳定解都是二维Bogomolnyi涡旋。
英文摘要：
We classify entire stable solutions with quadratic energy growth in the $4$-dimensional abelian Higgs model. More precisely, we prove that such solutions are holomorphic with respect to some complex structure, namely they satisfy the first order equations introduced by Bradlow, and consequently their nodal sets are holomorphic curves. Conversely, we construct solutions whose nodal set is any prescribed holomorphic curve with quadratic area growth. As a corollary, we show that all stable solutions with linear energy growth in $\mathbb{R}^3$ are two-dimensional Bogomolnyi vortices.
