  By explicitly allowing for topology to change as a function of time,
two-dimensional quantum gravity defined through causal dynamical triangulations
gives rise to a new continuum string field theory. Within a matrix-model
formulation we show that -- rather remarkably -- the associated sum over all
genera can be performed in closed form, leading to a nonperturbative definition
of CDT string field theory. We also obtain explicit formulas for the n-loop
correlation functions. Our construction exhibits interesting parallels with
previous, purely Euclidean treatments.
