Existence of dyons in minimally gauged Skyrme model via constrained minimization

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• 作者：Zhifeng Gao^a ; ^{gzf@henu.edu.cn} ; Yisong Yang^b ; ^{yyang@math.poly.edu}
• 关键词：Skyrme model ; Gauge fields ; Electromagnetism ; Monopoles ; Dyons ; Topological invariants ; Calculus of variations for indefinite action functional ; Constraints ; Weak convergence
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：15 April, 2012
• 卷：262
• 期：8
• 页码：3602-3625
• 文件大小：199 K

摘要

We prove the existence of electrically and magnetically charged particle-like static solutions, known as dyons, in the minimally gauged Skyrme model developed by Brihaye, Hartmann, and Tchrakian. The solutions are spherically symmetric, depend on two continuous parameters, and carry unit monopole and magnetic charges but continuous Skyrme charge and non-quantized electric charge induced from the 始t Hooft electromagnetism. The problem amounts to obtaining a finite-energy critical point of an indefinite action functional, arising from the presence of electricity and the Minkowski spacetime signature. The difficulty with the absence of the Higgs field is overcome by achieving suitable strong convergence and obtaining uniform decay estimates at singular boundary points so that the negative sector of the action functional becomes tractable.