Effective String Theory (EST) represents a powerful non-perturbative approach to describe confinement in Yang-Mills theory that models the confining flux tube as a thin vibrating string. EST calculations are usually performed using the zeta-function regularization: however there are situations (for instance the study of the shape of the flux tube or of the higher order corrections beyond the Nambu-Goto EST) which involve observables that are too complex to be addressed in this way. In this paper we propose a numerical approach based on recent advances in machine learning methods to circumvent this problem. Using as a laboratory the Nambu-Goto string, we show that by using a new class of deep generative models called Continuous Normalizing Flows it is possible to obtain reliable numerical estimates of EST predictions.

翻译：有效弦论（EST）是一种描述杨-米尔斯理论中禁闭现象的强大非微扰方法，它将禁闭通量管建模为细振动弦。EST计算通常采用zeta函数正则化方法，然而在某些情况下（例如研究通量管形状或Nambu-Goto弦理论高阶修正），涉及的观测量过于复杂而难以通过该方法处理。本文提出一种基于机器学习最新进展的数值方法来解决此问题。以Nambu-Goto弦为研究平台，我们证明通过使用名为连续归一化流的新型深度生成模型，可以获得EST理论预测的可靠数值估计。