A Minimal Length from the Cutoff Modes in Asymptotically Safe Quantum Gravity

TL;DR

This paper investigates how asymptotically safe Quantum Einstein Gravity may lead to a dynamically generated minimal length scale, manifesting as a minimal angular resolution on a quantum 4-sphere, despite no minimal proper length.

Contribution

It demonstrates that QEG induces a minimal angular resolution, revealing a form of 'fuzziness' in the quantum spacetime structure without a minimal proper length.

Findings

QEG's cutoff modes imply a minimal angular separation.

The quantum 4-sphere exhibits 'fuzziness' at small scales.

No minimal proper length is found, but a minimal angular resolution exists.

Abstract

Within asymptotically safe Quantum Einstein Gravity (QEG), the quantum 4-sphere is discussed as a specific example of a fractal spacetime manifold. The relation between the infrared cutoff built into the effective average action and the corresponding coarse graining scale is investigated. Analyzing the properties of the pertinent cutoff modes, the possibility that QEG generates a minimal length scale dynamically is explored. While there exists no minimal proper length, the QEG sphere appears to be "fuzzy" in the sense that there is a minimal angular separation below which two points cannot be resolved by the cutoff modes.