Fractal Space-times Under the Microscope: a RG View on Monte Carlo Data

          @misc{ pirsa_PIRSA:12020088,
            doi = {10.48660/12020088},
            url = {https://pirsa.org/12020088},
            author = {Saueressig, Frank},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Fractal Space-times Under the Microscope: a RG View on Monte Carlo Data},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {feb},
            note = {PIRSA:12020088 see, \url{https://pirsa.org}}
          }
          

Abstract

The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In particular the spectral dimension, which measures the return probability of a fictitious diffusion process on space-time, provides a valuable probe which is easily accessible both in the continuum functional renormalization group and discrete Monte Carlo simulations of the gravitational action. In this talk, I will give a detailed exposition of the fractal properties associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). Comparing these continuum results to three-dimensional Monte Carlo simulations, we demonstrate that the resulting spectral dimensions are in very good agreement. This comparison also provides a natural explanation for the apparent conflicts between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.