Abstract
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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Acknowledgments
We thank M. Panero, S. Bacchio, A. Bulgarelli, K. A. Nicoli and A. Smecca for several insightful discussions. We acknowledge support from the SFT Scientific Initiative of INFN. This work was partially supported by the Simons Foundation grant 994300 (Simons Collaboration on Confinement and QCD Strings) and by the Prin 2022 grant 2022ZTPK4E. We thank ECT* and the ExtreMe Matter Institute EMMI at GSI, Darmstadt, for support in the framework of an ECT*/EMMI Workshop during which this work has been completed.
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Caselle, M., Cellini, E. & Nada, A. Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows. J. High Energ. Phys. 2024, 48 (2024). https://doi.org/10.1007/JHEP02(2024)048
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DOI: https://doi.org/10.1007/JHEP02(2024)048