Generalization of the relativistic string model and the topological structure of its clasical solutions

A generalization of the Nambu relativistic string action taking into account the topological invariant ∫∫R√-g dtaudsigma is proposed. It is shown that this generalization solves the problem of infinite boundary conditions for the Nambu string in the Regge-Lund-Omnes geometric approach. The presence of a hidden topological structure of the string action extremums, realized on the static solutions of the generalized model, is shown. The energy spectrum of the polarized string connected with this topological structure is found to be hydrogen-like. (orig.)