论文标题
用任意维度耗尽BPS域墙网络的所有精确解决方案
Exhausting all exact solutions of BPS domain wall networks in arbitrary dimensions
论文作者
论文摘要
我们在具有$ n $复杂标量字段的扩展Abelian-Higgs模型中获得了通用非平面BPS网络的完整模量参数，并用相应的$ \ MathBb {C} p^{n -1} $模型中的所有精确解决方案耗尽所有精确解决方案。我们通过网格图开发了一个方便的描述，该描述是由模型的质量参数确定的多面体。为了说明我们方法的有效性，我们以$ 3+1 $尺寸为较低的$ n $来制定非平面域墙网络。通常，当网格图的多面体具有内部顶点，并且可以通过模量参数控制，网络可以具有紧凑的真空气泡，这些真空气泡是被域壁包围的有限真空区域。我们还构建了带有气泡的域墙网络，在柏拉图式，阿基赛马，加泰罗尼亚和开普勒poinsot固体的形状中。
We obtain full moduli parameters for generic non-planar BPS networks of domain walls in an extended Abelian-Higgs model with $N$ complex scalar fields, and exhaust all exact solutions in the corresponding $\mathbb{C}P^{N -1}$ model. We develop a convenient description by grid diagrams which are polytopes determined by mass parameters of the model. To illustrate the validity of our method, we work out non-planar domain wall networks for lower $N$ in $3+1$ dimensions. In general, the networks can have compact vacuum bubbles, which are finite vacuum regions surrounded by domain walls, when the polytopes of the grid diagrams have inner vertices, and the size of bubbles can be controlled by moduli parameters. We also construct domain wall networks with bubbles in the shapes of the Platonic, Archimedean, Catalan, and Kepler-Poinsot solids.
