Fractal universe and quantum gravity

TL;DR

This paper introduces a fractal spacetime field theory that is Lorentz invariant, renormalizable, and finite, with potential implications for quantum gravity and cosmology, by describing a flow from a fractal ultraviolet regime to standard four-dimensional physics.

Contribution

It presents a novel fractal spacetime field theory that is Lorentz invariant and renormalizable, connecting fractal ultraviolet behavior to conventional physics.

Findings

The theory is Lorentz invariant and power-counting renormalizable.

Spacetime exhibits a flow from a fractal dimension 2 in the ultraviolet to four in the infrared.

Implications for quantum gravity and the cosmological constant are discussed.

Abstract

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.