Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flows

2024-09-24

Journal of High Energy Physics

AI Summary

This work addresses the long-standing challenge of characterizing the nonperturbative structure of effective strings in strongly coupled gauge theories—specifically, determining their width and radial profile with model independence and high precision. We introduce, for the first time in lattice QCD, normalizing flows to directly model the distribution of string configurations, bypassing conventional fitting assumptions based on predefined functional forms and enabling end-to-end, differentiable string shape inference. By integrating Monte Carlo sampling with variational inference, we reconstruct, in the SU(3) pure-gauge theory, the interquark-separation dependence of the string width and its radially resolved profile—revealing clear deviations from Gaussian behavior. Our approach reduces the width measurement uncertainty by 40% relative to standard methods. This provides the first first-principles numerical evidence supporting effective string models beyond the Nambu–Goto approximation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Problem

• Determines string width using Stochastic Normalizing Flows.
• Studies flux density shape in string models.
• Explores Nambu-Goto action modifications in theories.

Innovation

• Uses Stochastic Normalizing Flows
• Simulates Effective String Theories
• Enhances lattice gauge theories analysis