Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows
This addresses a computational bottleneck for researchers in theoretical physics studying confinement in Yang-Mills theory, offering a novel method for handling complex observables beyond traditional zeta-function regularization.
The paper tackled the problem of complex observables in Effective String Theory (EST) by proposing a numerical approach using Continuous Normalizing Flows, which provided reliable numerical estimates for predictions in the Nambu-Goto string model.
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.