Sampling Nambu-Goto theory using Normalizing Flows

TL;DR

This paper demonstrates the use of Physics-Informed Stochastic Normalizing Flows to efficiently sample the Nambu-Goto string action in Effective String Theory, providing a new numerical approach for studying confinement in Yang-Mills theory.

Contribution

It introduces a novel application of Normalizing Flows to lattice Effective String Theory, enabling efficient sampling and validation of theoretical conjectures.

Findings

Successful sampling of Nambu-Goto string using NFs

Validation of analytical results as benchmarks

Numerical evidence supporting a string width conjecture

Abstract

Effective String Theory (EST) is a non-perturbative framework used to describe confinement in Yang-Mills theory through the modeling of the interquark potential in terms of vibrating strings. An efficient numerical method to simulate such theories where analytical studies are challenging is still lacking. However, in recent years a new class of deep generative models called Normalizing Flows (NFs) has been proposed to sample lattice field theories more efficiently than traditional Monte Carlo methods. In this contribution, we show a proof of concept of the application of NFs to EST regularized on the lattice. Namely, we introduce Physics-Informed Stochastic Normalizing Flows and we use them to sample the Nambu-Goto string action with two goals: use the known analytical results of this theory as a benchmark and demonstrate the efficiency of our method in obtaining new results of physical interest and in particular in providing a numerical proof for a conjecture regarding the width of the string.