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We present a study of the effective string that describes the infrareddynamics of SU(2) Yang-Mills theory in three dimensions. By combininghigh-precision lattice simulation results for Polyakov-loop correlators atfinite temperatures close to (and less than) the deconfinement one with theanalytical constraints from renormalization-group arguments, from the exactintegrability of the two-dimensional Ising model that describes theuniversality class of the critical point of the theory, from conformalperturbation theory, and from Lorentz invariance, we derive tight quantitativebounds on the corrections to the effective string action beyond the Nambu-Gotoapproximation. We show that these corrections are compatible with thepredictions derived from a bootstrap analysis of the effective string theory,and have a value which does not allow to prove the Axionic String Ansatz forthis model

Fine corrections in the effective string describing SU(2) Yang-Mills theory in three dimensions