Asymptotic Safety in Quantum Einstein Gravity: nonperturbative   renormalizability and fractal spacetime structure
  The asymptotic safety scenario of Quantum Einstein Gravity, the quantum field theory of the spacetime metric, is reviewed and it is argued that the theory is likely to be nonperturbatively renormalizable. It is also shown that asymptotic safety implies that spacetime is a fractal in general, with a fractal dimension of 2 on sub-Planckian length scales. 
O. Lauscher, M. Reuter