Light cone quantization of the c=2 matrix model

We study the large N limit of an interacting two-dimensional matrix field theory, whose perturbative expansion generates the sum over planar random graphs embedded in two-dimensions. In the light cone quantization the theory possesses closed string excitations which become free as N→∞. If the longitudinal momenta are discretized, then the calculation of the free string spectrum reduces to finite matrix diagonalization, the size of the matrix growing as the cut-off is removed. Our numerical results suggest that, for a critical coupling, the light cone string spectrum becomes continuous. This would indicate the massless dynamics of the Liouville mode of two-dimensional gravity, which would constitute a third dimension of the string theory.