Evidence for a Phase Transition in 2D Causal Set Quantum Gravity

TL;DR

This paper provides evidence for a phase transition in 2D causal set quantum gravity, showing a shift between continuum and crystalline phases influenced by a non-locality parameter, with implications for the theory's continuum limit.

Contribution

It introduces a phase transition analysis in 2D causal set quantum gravity incorporating a non-locality parameter, revealing the phase structure and its dependence on temperature and non-locality.

Findings

Monotonically decreasing transition temperature with increasing epsilon.

Existence of a phase transition line asymptoting to infinite temperature.

Continuum phase persists beyond the phase transition line.

Abstract

We present evidence for a phase transition in a theory of 2D causal set quantum gravity which contains a dimensionless non-locality parameter $\epsilon \in (0,1]$. The transition is between a continuum phase and a crystalline phase, characterised by a set of covariant observables. For a fixed size of the causal set the transition temperature $\beta_c^{-1}$ decreases monotonotically with $\epsilon$. The line of phase transitions in the $\beta_c^2$ v/s $\epsilon$ plane asymptotes to the infinite temperature axis, suggesting that the continuum phase survives the analytic continuation.