AI 中文总结
研究阿贝尔 - 希格斯模型中宇宙弦上矢量激发的动力学，确定其频谱、分布及衰减特性，发现其与戈德斯通扇区存在参量不稳定性，构建有效模型捕捉该不稳定性，揭示矢量激发在局部弦动力学中有重要作用。
AI 中文摘要
我们研究了阿贝尔 - 希格斯模型中局域在宇宙弦上的矢量激发的动力学。这些受限规范场涨落表现为沿弦传播的大质量矢量自由度。我们表明，对于标量自耦合$\lambda$的所有值，它们都保持有界，包括先前研究的传统形状模式不再存在的参数区域。确定其频谱和空间分布后，我们分析其通过与体辐射的非线性耦合的衰减。其振幅呈现与非线性辐射相关的特征幂律弛豫。对于足够大的$\lambda$，标量辐射通道在运动学上不可达，衰减由准正则模式介导，可解释为弦的费什巴赫共振。然后我们研究矢量激发弦的完整$3 + 1$维动力学。场论模拟揭示了矢量模式与戈德斯通扇区之间的参量不稳定性。与形状模式不同，矢量模式同时共振激发两个横向方向。此外，我们构建了一个有效模型来捕捉这种不稳定性并确定其负责的非线性耦合。我们的结果表明，矢量激发构成了一个长寿命的大质量自由度，在局部弦的动力学中起重要作用。
英文摘要
We investigate the dynamics of vector excitations localized on cosmic strings in the Abelian-Higgs model. These confined gauge field fluctuations behave as massive vector degrees of freedom propagating along the string. We show that they remain bounded for all values of the scalar self coupling $λ$, including parameter regimes in which the previously studied conventional shape mode is no longer present. After determining their spectra and spatial profiles, we analyze their decay through nonlinear coupling to bulk radiation. Their amplitudes exhibit the characteristic power law relaxation associated with non-linear radiation. For sufficiently large $λ$ the scalar radiation channel becomes kinematically inaccessible and the decay is instead mediated by quasinormal modes which can be interpreted as Feshbach resonances of the string. We then study the full $3+1$ dimensional dynamics of the vector-excited string. Field theory simulations reveal a parametric instability between the vector mode and the Goldstone sector. In contrast to the shape mode, the vector mode resonantly excites both transverse directions simultaneously. In addition, we build an effective model that captures the instability and identifies the nonlinear couplings responsible for it. Our results show that vector excitations constitute a long-lived massive degree of freedom with a non-trivial role in the dynamics of local strings.
Comments45 pages, 16 figures
