Introduction to multifractional spacetimes

Abstract

We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display discrete symmetries in the ultraviolet and ordinary Poincaré symmetries in the infrared. Under certain reasonable assumptions, field theories (including gravity) on multifractional geometries are generally argued to be perturbatively renormalizable. We also sketch the relation with other field theories of quantum gravity based on the renormalization group.

26 pages, 6 figures; v2: references added. Lectures given at Sixth International School on Field Theory and Gravitation 2012 (Petropolis, Brazil)

References in corpus (4)

• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Fractal properties of quantum spacetime
• Fractional diffusion equations and processes with randomly varying time
• Trace Anomaly in Quantum Spacetime Manifold

Cited by in corpus (2)

• Symmetries and propagator in multifractional scalar field theory
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