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arXiv 2003.05899hep-th
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$SO(2)$在$4+1$维度上测量的Skyrmions

$SO(2)$ gauged Skyrmions in $4+1$ dimensions

Francisco Navarro-Lerida, Eugen Radu, D. H. Tchrakian

备注：
18 pages, 12 figures; matches version accepted in PRD
发表信息：
Phys. Rev. D 101, 125014 (2020)
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摘要：

我们研究了最简单的$SO(2)$规范$O(5)$ Skyrme模型在$4+1$（平坦）维度。在规范解耦极限下，该模型支持拓扑稳定的孤子（Skyrmions），并且在规范化后，解的静态能量由“重子数”从下而上有界。所研究的模型具有Maxwell和Maxwell-Chern-Simons动力学。所考虑的配置是在${\mathbb R}^4$子空间中的双方位角对称性，导致在一个二维子系统，以及在${\mathbb R}^4$子空间中的两个平面，这导致在一个一维子系统中的增强的对称性。在这两种情况下构造的数值解。在纯磁的情况下，完全双方位角的解决方案，而带电和自旋的解决方案只在径向（增强对称）的情况下，无论是在存在的陈-西蒙斯项，并在其缺席。我们发现，与类似的模型在$2+1$尺寸，在这里研究的模型中的Chern-Simons项的存在下，结果只在定量的影响。

英文摘要：

We study the simplest $SO(2)$ gauged $O(5)$ Skyrme models in $4+1$ (flat) dimensions. In the gauge decoupled limit, the model supports topologically stable solitons (Skyrmions) and after gauging, the static energy of the solutions is bounded from below by a "baryon number". The studied model features both Maxwell and Maxwell--Chern-Simons dynamics. The considered configurations are subject to bi-azimuthal symmetry in the ${\mathbb R}^4$ subspace resulting in a two dimensional subsystem, as well as subject to an enhanced symmetry relating the two planes in the ${\mathbb R}^4$ subspace, which results in a one dimensional subsystem. Numerical solutions are constructed in both cases. In the purely magnetic case, fully bi-azimuthal solutions were given, while electrically charged and spinning solutions were constructed only in the radial (enhanced symmetric) case, both in the presence of a Chern-Simons term, and in its absence. We find that, in contrast with the analogous models in $2+1$ dimensions, the presence of the Chern-Simons term in the model under study here results only in quantitative effects.

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