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arXiv 2001.07552hep-thastro-ph.COhep-ph
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任意维畴壁结的精确解

Exact solutions of domain wall junctions in arbitrary dimensions

Minoru Eto, Masaki Kawaguchi, Muneto Nitta, Ryotaro Sasaki

备注：
34 pages, 10 figures; Several comments and new reference were added
发表信息：
Phys. Rev. D 102, 065006 (2020)
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摘要：

在$(D+1)$维时空中，在扩展的Abelian-Higgs模型下，得到了静态、稳定、非平面BPS畴壁结的精确解析解.对于特定的质量参数的选择，拉格朗日是不变的对称组${\cal S}_{D+1}$的程度$D+1$自发地打破了${\cal S}_D$在真空中，承认${\cal S}_{D+1}/{\cal S}_D$域壁结。在$D=2$中，存在三个真空和三个畴壁在接合点处相遇，其中如之前已知的，对于BPS畴壁接合和BPS畴壁分别存在常规拓扑电荷$Y$和$Z$。在$D=3$中，有四个真空、六个畴壁、三个畴壁相遇的四条连接线和所有六个畴壁相遇的一个连接点。除了传统的拓扑电荷$Y$和$Z$外，我们定义了一个新的拓扑电荷$X$。在一般维数下，我们发现在$D$维实空间中表示的构形与在$D$维内部空间中的正则$D$ -单形是对偶的，并且正则$D$ -单形的$d$维子单形对应于$(D-d)$维交.对于$d$维次单形，拓扑荷被推广到$d$维壁荷$W_d$.

英文摘要：

Exact analytic solutions of static, stable, non-planar BPS domain wall junctions are obtained in extended Abelian-Higgs models in $(D+1)$-dimensional spacetime. For specific choice of mass parameters, the Lagrangian is invariant under the symmetric group ${\cal S}_{D+1}$ of degree $D+1$ spontaneously broken down to ${\cal S}_D$ in vacua, admitting ${\cal S}_{D+1}/{\cal S}_D$ domain wall junctions. In $D=2$, there are three vacua and three domain walls meeting at a junction point, in which the conventional topological charges $Y$ and $Z$ exist for the BPS domain wall junctions and the BPS domain walls, respectively as known before. In $D=3$, there are four vacua, six domain walls, four junction lines on which three domain walls meet, and one junction point on which all the six domain walls meet. We define a new topological charge $X$ for the junction point in addition to the conventional topological charges $Y$ and $Z$. In general dimensions, we find that the configuration expressed in the $D$-dimensional real space is dual to a regular $D$-simplex in the $D$-dimensional internal space and that a $d$-dimensional subsimplex of the regular $D$-simplex corresponds to a $(D-d)$-dimensional intersection. Topological charges are generalized to the level-$d$ wall charge $W_d$ for the $d$-dimensional subsimplexes.

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