论文标题
在任意维度中的域壁连接的确切解决方案
Exact solutions of domain wall junctions in arbitrary dimensions
论文作者
论文摘要
在$（d+1）$ - 尺寸时空的扩展Abelian-Higgs模型中获得静态，稳定，非平面BPS域壁连接的精确分析解决方案。对于质量参数的具体选择，Lagrangian在对称群体$ {\ cal s} _ {d+1} $ $ d $ d+1 $自发上分解为vacua中的$ {\ cal s} _d $ in Vacua中的$ {\ cal s} $ {\ cal s} _ {d+1+1} $ cl n in varemiant不变。在$ d = 2 $中，在一个接线点上有三个真空墙和三个域墙会议，在该点中，BPS域墙连接处和BPS域墙壁的常规拓扑费用$ y $和$ z $分别如前所述。在$ d = 3 $中，有四个真空吸尘器，六个域墙壁，四个域墙相遇的四个接线线以及所有六个域墙壁相遇的连接点。除了传统的拓扑费用$ y $和$ z $之外，我们还为接线点定义了新的拓扑费$ x $。一般而言，我们发现在$ d $维的真实空间中表达的配置对$ d $ d $维的内部空间中的常规$ d $ simplex是双重的，并且$ d $ d $维二$ d $ d $ d $ -smimplex对应于a $（d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d-d）$（d-d-d-d）$ - dimensionalssectionsectionsection。拓扑费用概括为$ d $ wall Charge $ w_d $，用于$ d $二维的子图案。
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.
