Gauge models of discrete strings

A new class of constrained hamiltonian systems with a finite number of degrees of freedom is proposed in which excitations can be divided into two groups analogous to the left and right movers of string theories. These models can be regarded as some discrete versions of the bosonic string, and in the continuum limit with the infinite dimensional constraint algebra Vect(Sl) x (lower case x) Vect(Sl) one can obtain the standard theory of closed bosonic strings. We also discuss the problem of quantizing these models and construct the propagator by using path integral methods. A possibility of a supersymmetric extension of our models (discrete fermionic strings) is also pointed out. 7 refs