A Causal Alternative for c=0 Strings

TL;DR

This paper explores a new continuum limit of the one-matrix model that models causal two-dimensional quantum gravity, revealing different geometric scaling and reproducing results from causal dynamical triangulations.

Contribution

It introduces a causal continuum limit for the one-matrix model, providing a geometric interpretation and connecting it to causal dynamical triangulations.

Findings

Geodesic distance scales canonically in the new limit

Results match those of causal dynamical triangulations

Provides a geometric interpretation of the model

Abstract

We review a recently discovered continuum limit for the one-matrix model which describes "causal" two-dimensional quantum gravity. The behaviour of the quantum geometry in this limit is different from the quantum geometry of Euclidean two-dimensional quantum gravity defined by taking the "standard" continuum limit of the one-matrix model. Geodesic distance and time scale with canonical dimensions in this new limit, contrary to the situation in Euclidean two-dimensional quantum gravity. Remarkably, whenever we compare, the known results of (generalized) causal dynamical triangulations are reproduced exactly by the one-matrix model. We complement previous results by giving a geometrical interpretation of the new model in terms of a generalization of the loop equation of Euclidean dynamical triangulations. In addition, we discuss the time evolution of the quantum geometry.