On the Quantum Geometry of Multi-critical CDT

TL;DR

This paper extends multi-critical Causal Dynamical Triangulations (CDT) to higher critical points, deriving continuum limits, calculating quantum geometric observables, and establishing a string field theory formalism consistent with matrix model loop equations.

Contribution

It introduces a higher multi-critical CDT model, computes the resolvent and propagator, and develops a string field theory framework aligned with matrix model results.

Findings

Continuum limit derived at higher multi-critical points

Resolvent computed for arbitrary multi-critical points

String field theory formalism consistent with matrix model loop equations

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.