关于3荷对称单极
On Charge 3 Symmetric Monopoles
摘要：
单极子是SU（2）规范理论在$\mathbb{R}^{3}$中的解，满足能量下限和某些渐近条件，这些条件转化为编码在其电荷中的拓扑性质。使用来自可积系统的方法，单极子可以通过它们的{谱曲线}，即代数曲线，以满足某些约束的两个复变量的多项式P给出，用代数几何术语来描述。在这篇论文中，我们专注于Ercolani-Sinha公式，其中P的系数必须满足Ercolani-Sinha约束，作为周期之间的关系。研究了一类特殊的单极子，即电荷为3的单极子，其对称性为$C_{3}$，3阶循环群。这类循环3-单极子描述的属4谱曲线$\hat{X}$，受到Ercolani-Sinha约束：本工作的目的是建立这样的单极子的存在，这转化为解决$\hat{X}$的Ercolani-Sinha约束。
英文摘要：
Monopoles are solutions of an SU(2) gauge theory in $\mathbb{R}^{3}$ satisfying a lower bound for energy and certain asymptotic conditions, which translate as topological properties encoded in their charge. Using methods from integrable systems, monopoles can be described in algebraic-geometric terms via their {spectral curve}, i.e. an algebraic curve, given as a polynomial P in two complex variables, satisfying certain constraints. In this thesis we focus on the Ercolani-Sinha formulation, where the coefficients of P have to satisfy the Ercolani-Sinha constraints, given as relations amongst periods. A particular class of such monopoles is studied, namely charge 3 monopoles with a symmetry by $C_{3}$, the cyclic group of order 3. This class of cyclic 3-monopoles is described by the genus 4 spectral curve $\hat{X}$, subject to the Ercolani-Sinha constraints: the aim of the present work is to establish the existence of such monopoles, which translates into solving the Ercolani-Sinha constraints for $\hat{X}$.
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。
