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The U(1) lattice gauge theory in three dimensions is a perfect laboratory tostudy the properties of the confining string. On the one hand, thanks to themapping to a Coulomb gas of monopoles, the confining properties of the modelcan be studied semi-classically. On the other hand, high-precision numericalestimates of Polyakov loop correlators can be obtained via a duality map to aspin model. This allowed us to perform high-precision tests of the universalbehavior of the effective string and to find macroscopic deviations withrespect to the expected Nambu-Goto predictions. These corrections could befitted with very good precision including a contribution (which is consistentwith Lorentz symmetry) proportional to the square of the extrinsic curvature inthe effective string action, as originally suggested by Polyakov. Performingour analysis at different values of $\beta$ we were able to show that this termscales as expected by Polyakov's solution and dominates in the continuum. Wealso discuss the interplay between the extrinsic curvature contribution and theboundary correction induced by the Polyakov loops.

Effective string description of the interquark potential in the 3D U(1) lattice gauge theory