Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows

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.

Comments: 1+28 pages, 11 figures; v2 1+29 pages, 12 figures, added discussion on the implications of this approach for EST modeling, added results on the comparison between CNF and HMC, matches published version