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 re-moved. 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.