We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in quantum Einstein gravity. Using the continuum approach based upon the effective average action, we summarize the state of the art of the field with a focus on the evidence supporting the existence of the non-trivial renormalization group fixed point at the heart of the construction. As an application, the multifractal structure of the emerging space-times is discussed in detail. In particular, we compare the continuum prediction for their spectral dimension with Monte Carlo data from the causal dynamical triangulation approach.
New Journal of Physics
- Pub Date:
- May 2012
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- 87 pages, 13 figures, review article prepared for the New Journal of Physics focus issue on Quantum Einstein Gravity