Dimensionally Restricted Causal Set Quantum Gravity: Examples in Two and Three Dimensions

TL;DR

This paper investigates non-perturbative causal set quantum gravity in two and three dimensions with non-trivial spatial topology, revealing a phase transition between action-dominated and entropy-dominated phases through MCMC simulations.

Contribution

It introduces a novel framework for causal set MCMC calculations and presents the first implementation of causal set dynamics restricted to three dimensions.

Findings

Identifies a phase transition separating action and entropy dominance.

Characterizes the action dominated phase by layered posets with high connectivity.

Shows causal sets in the entropy dominated phase are manifold-like.

Abstract

We study dimensionally restricted non-perturbative causal set quantum dynamics in $2$ and $3$ spacetime dimensions with non-trivial global spatial topology. The causal set sample space is generated from causal embeddings into spacetime lattices with global spatial topology $S^1$ and $T^2$ in $2$ and $3$ dimensions, respectively. The quantum gravity partition function over these sample spaces is studied using Markov Chain Monte Carlo (MCMC) simulations after analytic continuation. In both $2$ and $3$ dimensions we find a phase transition that separates the dominance of the action from that of the entropy. The action dominated phase is characterised by ``layered'' posets with a high degree of connectivity, while the causal sets in the entropy dominated phase are manifold-like. This phase transition is similar in character to that seen for the sample space of $2$-orders, which are topologically trivial, hence suggesting that this is a generic feature of dimensionally restricted sample spaces. The simulations use a newly developed framework for causal set MCMC calculations. Ours is the first implementation of a causal set dynamics restricted to $3$ dimensions.