Exploring the Phase Diagram of Lattice Quantum Gravity

TL;DR

This paper investigates a nonperturbative lattice quantum gravity model, demonstrating an extended 4D geometric phase with spectral and Hausdorff dimensions close to 4, potentially resolving key theoretical tensions.

Contribution

It shows that including a measure term in Euclidean dynamical triangulations yields a 4D phase with realistic dimensions, advancing understanding of quantum gravity phases.

Findings

Spectral dimension D_s = 4.04 +/- 0.26 at large scales

Hausdorff dimension D_H consistent with 4

Short distance spectral dimension D_s ~ 3/2

Abstract

We present evidence that a nonperturbative model of quantum gravity defined via Euclidean dynamical triangulations contains a region in parameter space with an extended 4-dimensional geometry when a non-trivial measure term is included in the gravitational path integral. Within our extended region we find a large scale spectral dimension of D_s = 4.04 +/- 0.26 and a Hausdorff dimension that is consistent with D_H = 4 from finite size scaling. We find that the short distance spectral dimension is D_s ~ 3/2, which may resolve the tension between asymptotic safety and holographic entropy scaling.