A model for emergence of space and time

Article history: Received 26 May 2015 Accepted 27 July 2015 Available online 31 July 2015 Editor: L. Alvarez-Gaumé We study string field theory (third quantization) of the two-dimensional model of quantum geometry called generalized CDT (“causal dynamical triangulations”). Like in standard non-critical string theory the so-called string field Hamiltonian of generalized CDT can be associated with W -algebra generators through the string mode expansion. This allows us to define an “absolute” vacuum. “Physical” vacua appear as coherent states created by vertex operators acting on the absolute vacuum. Each coherent state corresponds to specific values of the coupling constants of generalized CDT. The cosmological “time” only exists relatively to a given “physical” vacuum and comes into existence before space, which is created because the “physical” vacuum is unstable. Thus each CDT “universe” is created as a “Big Bang” from the absolute vacuum, its time evolution is governed by the CDT string field Hamiltonian with given coupling constants, and one can imagine interactions between CDT universes with different coupling constants (“fourth quantization”) © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.