Stochastic normalizing flows for Effective String Theory

TL;DR

This paper introduces Stochastic Normalizing Flows (SNFs), a scalable machine learning approach combining normalizing flows with stochastic updates, to study Effective String Theory and analyze flux tube shapes in lattice gauge theories.

Contribution

It presents SNFs as a novel, scalable method for studying EST, integrating flow-based samplers with stochastic thermodynamics, enabling new numerical investigations.

Findings

Numerical results on flux tube shape in EST

SNFs outperform traditional methods in efficiency

Demonstration of SNFs applicability to lattice gauge theories

Abstract

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.