Classical relativistic string as a two-dimensional $SO(1,1)\times SO(2)$ gauge model

It is shown that a relativistic string in four-dimensional space-time is isomorphic to a dosed sector of the 2-dimensional $SO(1,1)\times SO(2)$ gauge model. Nambu's string model is generalized in a way that makes it possible to eliminate the singular boundary conditions in the geometrical approach. It is shown that the sector of the gauge model isomorphic to the generalized string can be described by the solutions of the complex Liouville equation with linear periodic boundary conditions.