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Free keywords:
High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract:
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. It also allows us to
probe ultramicroscopic scales where spectral methods based on ordinary geometry
typically fail. Consequences for noncommutative field theories are discussed.
