  We present a study of the effective string that describes the infrared
dynamics of SU(2) Yang-Mills theory in three dimensions. By combining
high-precision lattice simulation results for Polyakov-loop correlators at
finite temperatures close to (and less than) the deconfinement one with the
analytical constraints from renormalization-group arguments, from the exact
integrability of the two-dimensional Ising model that describes the
universality class of the critical point of the theory, from conformal
perturbation theory, and from Lorentz invariance, we derive tight quantitative
bounds on the corrections to the effective string action beyond the Nambu-Goto
approximation. We show that these corrections are compatible with the
predictions derived from a bootstrap analysis of the effective string theory,
and have a value which does not allow to prove the Axionic String Ansatz for
this model
