  The U(1) lattice gauge theory in three dimensions is a perfect laboratory to
study the properties of the confining string. On the one hand, thanks to the
mapping to a Coulomb gas of monopoles, the confining properties of the model
can be studied semi-classically. On the other hand, high-precision numerical
estimates of Polyakov loop correlators can be obtained via a duality map to a
spin model. This allowed us to perform high-precision tests of the universal
behavior of the effective string and to find macroscopic deviations with
respect to the expected Nambu-Goto predictions. These corrections could be
fitted with very good precision including a contribution (which is consistent
with Lorentz symmetry) proportional to the square of the extrinsic curvature in
the effective string action, as originally suggested by Polyakov. Performing
our analysis at different values of $\beta$ we were able to show that this term
scales as expected by Polyakov's solution and dominates in the continuum. We
also discuss the interplay between the extrinsic curvature contribution and the
boundary correction induced by the Polyakov loops.
