We discuss extensions of a recently introduced model of multi-critical CDT to
higher multi-critical points. As in the case of pure CDT the continuum limit
can be taken on the level of the action and the resulting continuum surface
model is again described by a matrix model. The resolvent, a simple observable
of the quantum geometry which is accessible from the matrix model is calculated
for arbitrary multi-critical points. We go beyond the matrix model by
determining the propagator using the peeling procedure which is used to extract
the effective quantum Hamiltonian and the fractal dimension in agreement with
earlier results by Ambjorn et al. With this at hand a string field theory
formalism for multi-critical CDT is introduced and it is shown that the
Dyson-Schwinger equations match the loop equations of the matrix model. We
conclude by commenting on how to formally obtain the sum over topologies and a
relation to stochastic quantisation.Comment: 15 pages, 2 figures, improved discussion, some new results regarding
Hausdorff dimension, as publishe