具有实对称性破缺的$R^2 \times R^+$上的扩展Bogomolny方程
The extended Bogomolny equations on $R^2 \times R^+$ with real symmetry breaking
AI总结：
本文构造了$R^2 \times R^+$上满足广义Nahm极边界条件与实对称性破缺渐近条件的扩展Bogomolny方程的解，该解是Taubes与Dimakis所构造瞬子解的类似物。
摘要：
本文构造了$X = R^2 \times R^+$上满足特定边界条件与渐近条件的扩展Bogomolny方程的解。设$y$为$R^+$的坐标，大致而言，边界条件与渐近条件分别表示当$y \to 0$与$y \to \infty$时，解趋近于某一模型解。其中$y \to 0$时的边界条件称为广义Nahm极边界条件，$y \to \infty$时的渐近条件称为实对称性破缺条件。这些解可视为Taubes与Dimakis（采用不同方法）构造的瞬子解的类似物，不过后者满足不同的渐近条件。
英文摘要：
In this paper, we construct solutions to the extended Bogomolny equations on $X = R^2 \times R^+$ with certain boundary conditions and asymptotic conditions. Let $y$ be the coordinate of $R^+$. Roughly, both the boundary condition and the asymptotic condition say that a solution approaches to a certain model solution when $y \rightarrow 0$ and $y \rightarrow \infty$ resepctively. The boundary condition ($y \rightarrow 0$) is called generalized Nahm pole boundary condition and the asymptotic condition ($y \rightarrow \infty$) is called real symmetry breaking condition. The solutions should be thought as an analog of the instanton solutions that Taubes and Dimakis have created (using different methods), while their solutions satisfy a different asymptotic condition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
