  In U(1) lattice gauge theory in three spacetime dimensions, the problem of
confinement can be studied analytically in a semi-classical approach, in terms
of a gas of monopoles with Coulomb-like interactions. In addition, this theory
can be mapped to a spin model via an exact duality transformation, which allows
one to perform high-precision numerical studies of the confining potential.
Taking advantage of these properties, we carried out an accurate investigation
of the effective string describing the low-energy properties of flux tubes in
this confining gauge theory. We found striking deviations from the expected
Nambu-Goto-like behavior, and, for the first time, evidence for contributions
that can be described by a term proportional to the extrinsic curvature of the
effective string worldsheet. Such term is allowed by Lorentz invariance, and
its presence in the infrared regime of the U(1) model was indeed predicted by
Polyakov several years ago. Our results show that this term scales as expected
according to Polyakov's solution, and becomes the dominant contribution to the
effective string action in the continuum limit. We also demonstrate
analytically that the corrections to the confining potential induced by the
extrinsic curvature term can be related to the partition function of the
massive perturbation of a c=1 bosonic conformal field theory. The implications
of our results for SU(N) Yang-Mills theories in three and in four spacetime
dimensions are discussed.
