Geometric operators in the asymptotic safety scenario for quantum gravity

TL;DR

This paper investigates geometric operators like geodesic length and hypersurface volume within the Asymptotic Safety framework for quantum gravity, computing their anomalous dimensions and exploring implications for effective dimensionality.

Contribution

It provides the first computation of anomalous dimensions for geometric operators in the Asymptotic Safety scenario, highlighting potential dimensional reduction effects.

Findings

Geometric operators exhibit non-trivial anomalous dimensions.

Results suggest an effective reduction in dimensionality at high energies.

Subtleties in defining geometric operators are discussed.

Abstract

We consider geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gravity. We discuss the role of these operators from the Asymptotic Safety perspective, and compute their anomalous dimensions within the Einstein-Hilbert truncation. We also discuss certain subtleties arising in the definition of such geometric operators. Our results hint to an effective dimensional reduction of the considered geometric operators.