Fractal universe and quantum gravity

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.

4 pages. v2: typos corrected; v3: discussion improved, intuitive introduction added, matches the published version

References in corpus (6)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Quantum field theory, gravity and cosmology in a fractal universe
• Fractal properties of quantum spacetime
• Fractional Action-Like Variational Problems
• Renormalization group in Lifshitz-type theories

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