A String Field Theory based on Causal Dynamical Triangulations

TL;DR

This paper develops a string field theory based on Causal Dynamical Triangulations to model quantum gravity, enabling calculations of topology-changing processes and non-trivial space-time topologies.

Contribution

It introduces a third quantization framework for 2D quantum gravity via CDT, with Dyson-Schwinger equations for topology-changing amplitudes.

Findings

Formulated a string field theory for 2D quantum gravity

Derived Dyson-Schwinger equations for the theory

Illustrated iterative solutions for transition amplitudes

Abstract

We formulate the string field theory in zero-dimensional target space corresponding to the two-dimensional quantum gravity theory defined through Causal Dynamical Triangulations. This third quantization of the quantum gravity theory allows us in principle to calculate the transition amplitudes of processes in which the topology of space changes in time, and to include non-trivial topologies of space-time. We formulate the corresponding Dyson-Schwinger equations and illustrate how they can be solved iteratively.