Quantizing quantum Ricci curvature

TL;DR

This paper introduces quantum Ricci curvature as a geometric measure applicable to non-smooth quantum spaces and demonstrates its effectiveness in two-dimensional quantum gravity, revealing classical-like curvature properties.

Contribution

It extends the concept of quantum Ricci curvature to nonperturbative quantum gravity and validates its properties through numerical evaluation in dynamical triangulations.

Findings

Quantum Ricci curvature remains scalable and computable in quantum gravity.

The curvature in 2D quantum gravity matches that of a 5D sphere.

Properties of quantum Ricci curvature are robust in nonclassical geometries.

Abstract

Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are scalability, computability and robustness. We demonstrate that these properties continue to hold in the context of nonperturbative quantum gravity, by evaluating the quantum Ricci curvature numerically in two-dimensional Euclidean quantum gravity, defined in terms of dynamical triangulations. Despite the well-known, highly nonclassical properties of the underlying quantum geometry, its Ricci curvature can be matched well to that of a five-dimensional round sphere.