A c=1 phase transition in two-dimensional CDT/Horava-Lifshitz gravity?

TL;DR

This paper investigates a phase transition in two-dimensional causal dynamical triangulations (CDT) coupled with matter fields, revealing a higher order transition at c=1 and distinct geometric phases compared to traditional dynamical triangulations.

Contribution

It demonstrates a c=1 phase transition in 2D CDT with matter fields and compares the resulting geometric phases to those in dynamical triangulations.

Findings

Identifies a higher order phase transition at c=1 in 2D CDT.

Shows the geometric phase for c>1 in CDT differs from that in DT.

Uses massive Gaussian fields to monitor the central charge.

Abstract

We study matter with central charge $c >1$ coupled to two-dimensional (2d) quantum gravity, here represented as causal dynamical triangulations (CDT). 2d CDT is known to provide a regularization of (Euclidean) 2d Ho\v{r}ava-Lifshitz quantum gravity. The matter fields are massive Gaussian fields, where the mass is used to monitor the central charge $c$. Decreasing the mass we observe a higher order phase transition between an effective $c=0$ theory and a theory where $c>1$. In this sense the situation is somewhat similar to that observed for "standard" dynamical triangulations (DT) which provide a regularization of 2d quantum Liouville gravity. However, the geometric phase observed for $c >1$ in CDT is very different from the corresponding phase observed for DT.