Bosonic string with extrinsic curvature on the lattice

The addition of a term proportional to the extrinsic curvature to the Nambu-Goto action could "smooth" the surface described by this theory allowing a correspondence between the bosonic string and the infrared behavior of QCD. We explore this possibility by studying the properties of the model numerically. We find a first order phase transition as the coupling constant for extrinsic curvature is increased from zero. The weak coupling phase has an infinite Hausdorff dimension. We speculate about the possibility of turning this transition into second order by adding other couplings, so that a continuum theory of smooth strings can be defined.