Abstract
We investigate the consequences of adding a term proportional to the extrinsic curvature to the Nambu-Goto action, as suggested by Polyakov. A classical analysis of the equations of motion, constraint structure and hamiltonian of this system is performed. Quantum corrections are calculated in the mean field approximation for a large number of dimensions of the embedding space. The exact beta function of the new coupling constant in this limit is obtained; it possesses only one zero at the origin. Effects induced by adding a term that weights string configurations according to the number of self-intersections are discussed. We briefly comment on a similar proposal for free paths made recently.
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