On the Quantum Geometry of Multi-critical CDT

Abstract

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.

arXiv comment15 pages, 2 figures, improved discussion, some new results regarding Hausdorff dimension, as published

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• 2d CDT with gauge fields
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• A model for emergence of space and time
• A restricted dimer model on a 2-dimensional random causal triangulation
• Coupling Dimers to CDT
• The cylinder amplitude in the Hard Dimer model on 2D Causal Dynamical Triangulations
• Criticality at absolute zero from Ising model on two-dimensional dynamical triangulations
• Boundary States of the Potts Model on Random Planar Maps
• Critical region for an Ising model coupled to causal dynamical triangulations