用深度学习模拟弦理论，精准计算禁闭机制中的弦宽与形状。
Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flows
- 采用随机归一化流进行非平衡蒙特卡洛采样。
- 首次精确计算弦宽与通量密度分布，验证了新项的物理意义。
- 适合研究强相互作用粒子禁闭机制的物理学者和计算学家。
基于流的架构最近被证明是高效模拟格点正则化有效弦理论的有效工具，这些理论通常难以通过标准蒙特卡洛方法进行高效采样。本文利用基于非平衡蒙特卡洛模拟的前沿深度学习架构——随机归一化流，研究多种有效弦模型。通过与奈穆-戈托模型的精确结果对比，验证了该方法的可靠性。在此基础上，我们分析了难以解析求解的可观测量，如弦的宽度和通量密度分布。此外，还对超出奈穆-戈托作用量的项进行了新颖的数值研究，并深入讨论其在格点规范理论中的意义。这些结果共同实现了对不同格点规范理论中禁闭机制精细结构的定量描述。本工作确立了基于流的采样器在有效弦理论中的可靠性和可行性，为未来在更复杂模型上的应用铺平了道路。
原文摘要 · Abstract (English)
Flow-based architectures have recently proved to be an efficient tool for numerical simulations of Effective String Theories regularized on the lattice that otherwise cannot be efficiently sampled by standard Monte Carlo methods. In this work we use Stochastic Normalizing Flows, a state-of-the-art deep learning architecture based on non-equilibrium Monte Carlo simulations, to study different effective string models. After testing the reliability of this approach through a comparison with exact results for the Nambu-Gotō model, we discuss results on observables that are challenging to study analytically, such as the width of the string and the shape of the flux density. Furthermore, we perform a novel numerical study of Effective String Theories with terms beyond the Nambu-Gotō action, including a broader discussion on their significance for lattice gauge theories. The combination of these findings enables a quantitative description of the fine details of the confinement mechanism in different lattice gauge theories. The results presented in this work establish the reliability and feasibility of flow-based samplers for Effective String Theories and pave the way for future applications on more complex models.
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