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. Some of these models can be regarded as discrete analogs of the bosonic string, and in the continuum limit with the infinite dimensional constraint algebra Vect (S 1 )⊗ Vect (S 1 ) one can obtain the classical theory of closed bosonic strings. We also discuss the problem of quantizing these models and constructing the propagator by using path integral methods. A possibility of a supersymmetric extension of our models is also pointed out.