Stochastic normalizing flows for Effective String Theory

2024-12-26

AI Summary

Lattice simulations of quark–antiquark flux tubes in Effective String Theory (EST) suffer from severe sampling inefficiencies and poor convergence, particularly in the strong-coupling confining regime. Method: We introduce Stochastic Normalizing Flows (SNFs), a novel generative sampling framework that couples normalizing flows with stochastic thermodynamic updates—marking the first integration of invertible deep generative models with non-equilibrium lattice field dynamics. SNFs incorporate physics-informed regularization from lattice gauge theory and explicitly model non-equilibrium evolution. Contribution/Results: SNFs dramatically improve sampling efficiency and statistical precision over conventional MCMC methods. For the first time, they enable high-accuracy extraction of key physical observables—including the transverse profile of the confining flux tube—directly from first-principles lattice data. The approach demonstrates exceptional generalization across coupling regimes and maintains full interpretability through its physically grounded architecture, establishing a scalable, principled paradigm for non-equilibrium sampling in strongly coupled quantum systems.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• Effective String Theory
• Machine Learning
• Quark-Antiquark Flux Tube

Innovation

• Stochastic Normalizing Flows
• Effective String Theory
• Thermodynamic Integration