Effective String Theory (EST) is a powerful tool used to study confinement in pure gauge theories by modeling the confining flux tube connecting a static quark-anti-quark pair as a thin vibrating string. Recently, flow-based samplers have been applied as an efficient numerical method to study EST regularized on the lattice, opening the route to study observables previously inaccessible to standard analytical methods. Flow-based samplers are a class of algorithms based on Normalizing Flows (NFs), deep generative models recently proposed as a promising alternative to traditional Markov Chain Monte Carlo methods in lattice field theory calculations. By combining NF layers with out-of-equilibrium stochastic updates, we obtain Stochastic Normalizing Flows (SNFs), a scalable class of machine learning algorithms that can be explained in terms of stochastic thermodynamics. In this contribution, we outline EST and SNFs, and report some numerical results for the shape of the flux tube.

翻译：有效弦论（EST）是一种研究纯规范理论中禁闭现象的有力工具，其将连接静态夸克-反夸克对的禁闭通量管建模为细小的振动弦。近期，基于流的采样器作为一种高效数值方法被应用于格点正则化的EST研究，为探索传统解析方法无法处理的观测量开辟了新途径。基于流的采样器是一类基于归一化流（NFs）的算法，后者是深度生成模型，近年来被提出作为格点场论计算中传统马尔可夫链蒙特卡罗方法的有前景的替代方案。通过将NF层与非平衡随机更新相结合，我们得到了随机归一化流（SNFs）——一类可扩展的机器学习算法，其原理可用随机热力学进行解释。本文概述了EST与SNFs的基本原理，并报告了通量管形状的部分数值计算结果。