A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations

TL;DR

This paper demonstrates that a matrix model can reproduce the Dyson-Schwinger equations of a novel 2D quantum gravity theory based on Causal Dynamical Triangulations, linking it to string field theory and the Dijkgraaf-Vafa correspondence.

Contribution

It shows that a cubic matrix model captures the Dyson-Schwinger equations of a new continuum 2D quantum gravity theory derived from Causal Dynamical Triangulations.

Findings

Matrix model reproduces Dyson-Schwinger equations

No fine-tuning needed for continuum limit

Connects quantum gravity with string field theory and matrix models

Abstract

A novel continuum theory of two-dimensional quantum gravity, based on a version of Causal Dynamical Triangulations which incorporates topology change, has recently been formulated as a genuine string field theory in zero-dimensional target space (arXiv:0802.0719). Here we show that the Dyson-Schwinger equations of this string field theory are reproduced by a cubic matrix model. This matrix model also appears in the so-called Dijkgraaf-Vafa correspondence if the superpotential there is required to be renormalizable. In the spirit of this model, as well as the original large-N expansion by 't Hooft, we need no special double-scaling limit involving a fine tuning of coupling constants to obtain the continuum quantum-gravitational theory. Our result also implies a matrix model representation of the original, strictly causal quantum gravity model.