Confining strings in three-dimensional gauge theories beyond the Nambu--Gotō approximation

We carry out a systematic study of the effective bosonic string describing confining flux tubes in \(\mathrm{SU}(N)\) Yang--Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu--Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with \(N=3\) and \(6\) color charges, and report an improved estimate for the \(N=2\) case, discussing the approach to the large-\(N\) limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky--Yaffe conjecture for the \(\mathrm{SU}(3)\) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky--Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.