Gravity on a multifractal

TL;DR

This paper explores the idea that spacetime behaves as a multifractal, being four-dimensional at large scales and two-dimensional at small scales, with implications for quantum gravity, particle physics, and cosmology.

Contribution

It introduces the concept of a multifractal spacetime with scale-dependent dimensions, linking fractal geometry to quantum gravity models.

Findings

Spacetime may be effectively two-dimensional at ultraviolet scales.

Multifractal structure impacts particle physics and cosmological models.

Supports the idea of dimensional reduction as a feature of quantum gravity.

Abstract

Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of these models of Nature. Thus motivated, we entertain the idea that spacetime is a multifractal with integer dimension 4 at large scales, while it is two-dimensional in the ultraviolet. Consequences for particle physics, gravity and cosmology are discussed.