Fractal spacetime structure in asymptotically safe gravity

By O. Lauscher, Martin Reuter. 2005

301 citations recorded by the source corpus.

Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7ff6b96ce574e7c1487fff7f1b78ed0bf49edd5d

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

The asymptotic safety scenario in quantum gravity: an introduction (2006, background): “Here only the fact is needed that the average 〈e−En(q)T 〉 can approximately be evaluated as [96, 97]”
Quantum field theory, gravity and cosmology in a fractal universe (2010, result): “This is in intriguing accordance with other proposals for quantum gravity such as causal dynamical triangulations [9], asymptotically safe gravity [10] and spin-foam models [11] (see also [12]).”
Nonperturbative quantum gravity (2012, background): “This anomalous scaling near the fixed point is the reason why the spectral dimension in both the asymptotic safety and the Hořava-Lifshiz scenario is 2 and not 4 [97, 111].”
The Asymptotic Safety Scenario in Quantum Gravity (2006, background): “This leads to a variant [157] of the argument first used in [135, 134]).”
The nonperturbative functional renormalization group and its applications (2020, methodology): “Indications for a reduction from d = 4 to d = 2 exist in the ultraviolet in the spectral dimension which is extracted from an RG improved diffusion equation [1263–1266].”
Cosmology of the Lifshitz universe (2009, background): “On the other hand, the spectral dimension(2) is particularly suitable for capturing the fractal behaviour of 2D Euclidean quantum gravity [71, 72, 75, 76, 77] (see also [78]–[81] for some formal studies on random geometrical objects), CDT [38, 39], asymptotically safe gravity [24], LQG and spin-foam”
Quantum-Spacetime Phenomenology (2008, result): “Two spectral dimensions for small diffusion times was then also found in studies inspired by asymptotic safety [360, 467] and studies based on Hořava–Liftschitz gravity [290].”