双曲2单极子的希钦与萨特克利夫度量
The Hitchin and Sutcliffe metrics for hyperbolic 2-monopoles
AI总结：
该研究对比双曲SU(2)双单极子的Hitchin与Sutcliffe度量，证明二者共形不等价、动力学预测不同，检验Sen猜想时发现Hitchin度量的$L^2$调和2-形式符合猜想，且Sutcliffe度量不收敛于Franchetti-Ross点粒子近似。
AI中文摘要：
我们比较两种当前已知的双曲SU(2)双单极子度量实例，以及它们作为双曲单极子动力学模型的候选资格。第一种是Sutcliffe（萨特克利夫）的边界度量，另一种是希钦（Hitchin）发现的著名自对偶爱因斯坦度量。我们证明这些度量是共形不等价的，且对单极子动力学的预测存在显著差异。我们将每种度量与双曲单极子动力学的Franchetti-Ross点粒子近似进行比较，发现Sutcliffe的度量在大分离极限下不会收敛到该点粒子近似。我们还通过计算每种度量的$L^2$调和2-形式来检验Sen（森）猜想，利用对称性论证可证明，Hitchin的度量具有一个符合该猜想的$L^2$调和2-形式。
英文摘要：
We compare two currently known examples of hyperbolic SU(2) two-monopole metrics and their candidacy as models of hyperbolic monopole dynamics. The first is Sutcliffe's boundary metric and the other is a well-known self-dual Einstein metric found by Hitchin. We show that these metrics are conformally inequivalent and make significantly different predictions for monopole dynamics. We compare each metric to the Franchetti-Ross point particle approximation of hyperbolic monopole dynamics. We show Sutcliffe's metric does not converge to the point particle approximation in the large separation limit. We also check Sen's conjecture for each metric by computing their $L^2$ harmonic two-forms. By a symmetry argument we are able to show that Hitchin's metric has a single $L^2$ harmonic two-form consistent with the conjecture.
