1203.5034 (Max R. Atkin et al.)

On the Quantum Geometry of Multi-critical CDT    [PDF]

Max R. Atkin, Stefan Zohren

We extend a recently introduced model of multi-critical CDT to higher multi-critical points. It is observed that the continuum limit can be taken on the level of the action and that 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 Hausdorff dimension. 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.

View original: http://arxiv.org/abs/1203.5034