# Imprint of quantum gravity in the dimension and fabric of spacetime

## TL;DR

This paper explores the connection between quantum gravity effects, like dimensional flow and spacetime fuzziness, using multifractional theories to show how scale-dependent dimensions lead to fuzzy, stochastic spacetime structures.

## Contribution

It introduces a novel link between dimensional flow and spacetime fuzziness within multifractional theories, supported by evidence and parameter fixing consistent with quantum gravity insights.

## Key findings

- Scale-dependent deformation of spacetime measure
- Fixing of free parameters using Planckian uncertainties
- Ultraviolet dimension aligns with other quantum gravity results

## Abstract

We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within the framework of multifractional theories, whose key assumption is an anomalous scaling of the spacetime dimension in the ultraviolet and a slow change of the dimension in the infrared. This sole ingredient is enough to produce a scale-dependent deformation of the integration measure with also a fuzzy spacetime structure. We also compare the multifractional correction to lengths with the types of Planckian uncertainty for distance and time measurements that was reported in studies combining quantum mechanics and general relativity heuristically. This allows us to fix two free parameters of the theory and leads, in one of the scenarios we contemplate, to a value of the ultraviolet dimension which had already found support in other quantum-gravity analyses. We also formalize a picture such that fuzziness originates from a fundamental discrete scale invariance at short scales and corresponds to a stochastic spacetime geometry.