Non-critical light-cone string Original Research Article

A free string quantum model is constructed directly in the light-cone variables in the range of dimensions 1 < D < 25. The longitudinal degrees of freedom are described by an abstract Verma module with the central charge restricted by the requirement of closure of the non-linear realization of the Poincaré algebra. The spin content of the model is analyzed. In particular for D = 4 the explicit formulae for the character generating functions of the open and closed strings are given and the spin spectrum of the first twelve excited levels is calculated. It is shown that for the space-time dimension in the range 1 < D < 25 this light-cone quantum model is equivalent to the critical massive string and to the non-critical Nambu-Goto string.