  Causal dynamical triangulations (CDT) can be used as a regularization of
quantum gravity. In two dimensions the theory can be solved anlytically, even
before the cut-off is removed and one can study in detail how to take the
continuum limit. We show how the CDT theory is related to Euclidean 2d quantum
gravity (Liouville quantum gravity), how it can be generalized and how this
generalized CDT model has a string field theory representation as well as a
matrix model representationof a new kind, and finally how it examplifies the
possibility that time in quantum gravity might be the stochastic time related
to the branching of space into baby universes.
