A model for emergence of space and time

TL;DR

This paper develops a string field theory framework for generalized causal dynamical triangulations (CDT) in two-dimensional quantum geometry, revealing how space and time emerge from an absolute vacuum through coherent states and vacuum instabilities.

Contribution

It introduces a string field Hamiltonian linked to W-algebra generators for generalized CDT, defining physical vacua as coherent states and explaining the emergence of space and time.

Findings

Space and time emerge from vacuum instabilities.

Physical vacua are coherent states created by vertex operators.

Multiple universes can interact via different coupling constants.

Abstract

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")