Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows

In the last few years Effective String Theory (EST) has emerged as a highly promising approach for the understanding and modeling of the non-perturbative behavior of confining Yang-Mills theories. In this framework, the confining flux tube that connects a quark-antiquark pair is represented as a thin vibrating string [1, 2]. In D 26, where D are the space-time dimensions of the target Lattice Gauge Theory (LGT), the EST (at least in its simplest formulation) is anomalous at the quantum level and thus must be considered only as an effective, large-distance description of Yang-Mills theories. Notwithstanding this, precise Monte Carlo simulations of several different LGTs proved that it is indeed a highly predictive effective model (for recent reviews see for instance [3, 4]). The reason of this success is in the so called "low energy universality" [3, 5-9] which states that, due to the symmetry constraints imposed by the Poincaré invariance in the target space, the first few terms of the EST large-distance expansion are universal and coincide with those of the Nambu-Goto action [1].