AI 中文总结
研究在特定标量场模型中\(\mathbb{Z}_N\)弦网络的形成与演化，通过经典晶格模拟，发现\(N = 2 - 8\)时网络趋近标度区域，弦密度与\(N^2 - 1\)成比例，得出引力波能量密度振幅标度与\(\mu^2 (N^2 - 1)^2\)相关的结论。
AI 中文摘要
我们在一个真空流形为\(\mathrm{PSU}(N)=\mathrm{SU}(N)/\mathbb{Z}_N\)的标量场模型中，对具有多弦结的全局\(\mathbb{Z}_N\)弦网络进行了数值研究。该模型的构建受质量变形的\(\mathcal{N}=4\)超对称杨 - 米尔斯理论（即\(\mathcal{N}=1^*\)理论）的希格斯真空启发，能有效描述具有重子顶点状结的弦网络。我们在辐射主导的宇宙中对这些网络的形成和演化进行了经典晶格模拟。对于\(N = 2,3,4,5\)和\(8\)，发现网络趋近标度区域而非陷入困境。弦密度的归一化与伴随表示的维度\(N^2 - 1\)成比例增长，非最小电荷分量仍占次要地位。这些结果表明，至少对于\(N\lesssim 8\)，宇宙弦网络产生的引力波能量密度振幅标度为\(\Omega_{\rm GW}\propto \mu^2 (N^2 - 1)^2\)，其中\(\mu\)是单位电荷弦的张力。
英文摘要
We numerically investigate networks of global $\mathbb{Z}_N$ strings with multi-string junctions in a scalar field model whose vacuum manifold is $\mathrm{PSU}(N)=\mathrm{SU}(N)/\mathbb{Z}_N$. The construction of the model is motivated by the Higgs vacua of mass-deformed $\mathcal{N}=4$ supersymmetric Yang-Mills theory, commonly known as $\mathcal{N}=1^*$ theory, and provides a tractable effective description of string networks with baryon-vertex-like junctions. We perform classical lattice simulations of the formation and evolution of these networks in a radiation-dominated universe. For $N=2,3,4,5,$ and $8$, we find that the networks approach a scaling regime rather than becoming frustrated. The normalization of the string density grows in proportion to the dimension of the adjoint representation, $N^2-1$, while non-minimal-charge components remain subdominant. These results imply that, at least for $N\lesssim 8$, the amplitude of the gravitational-wave energy density generated by the cosmic-string network scales as $Ω_{\rm GW}\propto μ^2 (N^2-1)^2$, where $μ$ is the tension of a unit-charge string.
Comments12 pages, 7 figures
