Discrete to continuum transition in multifractal spacetimes

Understand

We outline a field theory on a multifractal spacetime.

• The measure in the action is characterized by a varying Hausdorff dimension and logarithmic oscillations governed by a fundamental physical length.
• A fine hierarchy of length scales identifies different regimes, from a microscopic structure with discrete symmetries to an effectively continuum spacetime.
• Thanks to general arguments from fractal geometry, this scenario explicitly realizes two indirect or conjectured features of most quantum gravity models: a change of effective spacetime dimensionality with the probed scale, and the transition from a fundamentally discrete quantum spacetime to the continuum.