Quantum Flatness in Two-Dimensional CDT Quantum Gravity

TL;DR

This paper investigates quantum flatness in two-dimensional CDT quantum gravity, revealing a scale-independent quantum flatness that lacks a classical analogue, based on extensive Monte Carlo simulations.

Contribution

It introduces a criterion to distinguish local and global properties in 2D CDT quantum gravity and explores quantum flatness without a classical counterpart.

Findings

Quantum flatness is scale-independent in 2D CDT quantum gravity.

Monte Carlo simulations up to 600,000 building blocks show no classical flatness.

A new criterion differentiates local and topological properties of the quantum system.

Abstract

Flatness -- the absence of spacetime curvature -- is a well-understood property of macroscopic, classical spacetimes in general relativity. The same cannot be said about the concepts of curvature and flatness in nonperturbative quantum gravity, where the microscopic structure of spacetime is not describable in terms of small fluctuations around a fixed background geometry. An interesting case are two-dimensional models of quantum gravity, which lack a classical limit and therefore are maximally "quantum". We investigate the recently introduced quantum Ricci curvature in CDT quantum gravity on a two-dimensional torus, whose quantum geometry could be expected to behave like a flat space on suitably coarse-grained scales. On the basis of Monte Carlo simulations we have performed, with system sizes of up to 600.000 building blocks, this does not seem to be the case. Instead, we find a scale-independent "quantum flatness", without an obvious classical analogue. As part of our study, we develop a criterion that allows us to distinguish between local and global, topological properties of the toroidal quantum system.