Landau Theory of Causal Dynamical Triangulations

TL;DR

This paper applies Landau theory to Causal Dynamical Triangulations (CDT) to analyze phase structure and suggests the effective field theory aligns with foliation-preserving diffeomorphisms, hinting at connections to Horava-Lifshitz gravity.

Contribution

It introduces a Landau approach to CDT, identifying the volume of spatial slices as an order parameter and exploring the phase structure in two and three dimensions.

Findings

Volume of spatial slices acts as an order parameter.

Effective field theory likely respects foliation-preserving diffeomorphisms.

Hints at connections to Horava-Lifshitz gravity.

Abstract

Understanding the continuum limit of a theory of discrete random geometries is a beautiful but difficult challenge. In this optic, we review here the insights that can be obtained for Causal Dynamical Triangulations (CDT) by employing the Landau approach to critical phenomena. In particular, concentrating on the cases of two and three dimensions, we will make the case that the configuration of the volume of spatial slices effectively plays the role of an order parameter, helping us to understand the phase structure of CDT. Moreover, consistency with numerical simulations of CDT provides hints that the effective field theory of the model lives in the space of theories invariant under foliation-preserving diffeomorphisms. Among such theories, Horava-Lifshitz gravity has the special status of being a perturbatively renormalizable theory, while General Relativity sits in a subspace with enhanced symmetry. In order to reach either of them, one would likely need to fine tune some of the parameters in the CDT action, or additional ones from some generalization thereof.