  A novel continuum theory of two-dimensional quantum gravity, based on a
version of Causal Dynamical Triangulations which incorporates topology change,
has recently been formulated as a genuine string field theory in
zero-dimensional target space (arXiv:0802.0719). Here we show that the
Dyson-Schwinger equations of this string field theory are reproduced by a cubic
matrix model. This matrix model also appears in the so-called Dijkgraaf-Vafa
correspondence if the superpotential there is required to be renormalizable. In
the spirit of this model, as well as the original large-N expansion by 't
Hooft, we need no special double-scaling limit involving a fine tuning of
coupling constants to obtain the continuum quantum-gravitational theory. Our
result also implies a matrix model representation of the original, strictly
causal quantum gravity model.
