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Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows

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arxiv 2307.01107 v2 pith:3YEX6ZHV submitted 2023-07-03 hep-lat cs.LGhep-th

Michele Caselle , Elia Cellini , Alessandro Nada This is my paper · ORCID
classification hep-latcs.LGhep-th
keywords stringnambu-gotoapproachcontinuousflowsfluxmodelsnormalizing
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Effective String Theory (EST) represents a powerful non-perturbative approach to describe confinement in Yang-Mills theory that models the confining flux tube as a thin vibrating string. EST calculations are usually performed using the zeta-function regularization: however there are situations (for instance the study of the shape of the flux tube or of the higher order corrections beyond the Nambu-Goto EST) which involve observables that are too complex to be addressed in this way. In this paper we propose a numerical approach based on recent advances in machine learning methods to circumvent this problem. Using as a laboratory the Nambu-Goto string, we show that by using a new class of deep generative models called Continuous Normalizing Flows it is possible to obtain reliable numerical estimates of EST predictions.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stochastic Quantization as Optimal Control

    hep-lat 2026-07 conditional novelty 6.0 of 10

    Stochastic quantization is re-expressed as finite-time optimal control, in which a learned Doob force plus exact path weights reach the Gibbs measure without waiting for equilibrium.

  2. Studying Effective String Theory using deep generative models

    hep-lat 2025-08 conditional novelty 4.0 of 10

    Flow-based samplers numerically confirm the next-to-leading-order width and the resummed string-tension conjecture for the Nambu-Goto effective string in 2+1 dimensions.

  3. Symmetry-preserving neural networks in lattice field theories

    hep-lat 2025-06 conditional novelty 4.0 of 10

    Translation- and gauge-equivariant neural networks (L-CNNs) predict Wilson loops, topological charge, and flux observables with orders-of-magnitude lower error than symmetry-breaking baselines, and neural gradient flo...

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