arXiv 2006.017262020-06hep-thhep-ph

近BPS的小Skyrmions

Near-BPS baby Skyrmions

Sven Bjarke Gudnason, Marco Barsanti, Stefano Bolognesi

备注：: LaTeX: 55 pages, 23 figures; V2: comments and references added, typos corrected
发表信息：: JHEP 2011:062, 2020
DOI：: 10.1007/JHEP11(2020)062

摘要：

我们认为baby-Skyrme模型接近于所谓的限制baby-Skyrme模型，这是一个BPS模型与面积保持的同态不变性。微扰的形式是标准动力学狄利克雷项与一个小的系数$ε$。该模型的经典解，在$ε$中达到首阶，称为限制调和映射。在BPS极限（$ε\to 0$）下，单位拓扑荷的解是π介子。使用分析和数值参数，我们获得了大于一的拓扑扇区问题的解。我们在$ε$中发展了一个微扰格式，用它可以计算BPS质量的修正。首阶（$\mathcal{O}(ε^1)$）修正表明拓扑荷为2的Skyrmion子是能量优先的.结合能要求我们进入$ε$中的第三阶以捕获微扰理论中的相关项，然而，结合能在$ε^2$阶贡献总能量。我们发现，婴儿Skyrmions -在近BPS制度-是拓扑电荷2，在一个单一的点和相互接触的吸引力的通道中的方向在其周边的双光子。

英文摘要：

We consider the baby-Skyrme model in the regime close to the so-called restricted baby-Skyrme model, which is a BPS model with area-preserving diffeomorphism invariance. The perturbation takes the form of the standard kinetic Dirichlet term with a small coefficient $ε$. Classical solutions of this model, to leading order in $ε$, are called restricted harmonic maps. In the BPS limit ($ε\to 0$) of the model with the potential being the standard pion-mass term, the solution with unit topological charge is a compacton. Using analytical and numerical arguments we obtain solutions to the problem for topological sectors greater than one. We develop a perturbative scheme in $ε$ with which we can calculate the corrections to the BPS mass. The leading order ($\mathcal{O}(ε^1)$) corrections show that the baby Skyrmion with topological charge two is energetically preferred. The binding energy requires us to go to the third order in $ε$ to capture the relevant terms in perturbation theory, however, the binding energy contributes to the total energy at order $ε^2$. We find that the baby Skyrmions - in the near-BPS regime - are compactons of topological charge two, that touch each other on their periphery at a single point and with orientations in the attractive channel.

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