Scale dependant spectral dimension in models of causal quantum gravity
Dr. Stefan Zohren (Oxford University)

In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came from numerical results of four-dimensional causal dynamical triangulations (CDT). Since then little progress has been made in analytically understanding the numerical results coming from the CDT approach and showing that they remain valid when taking the continuum limit. In this talk we discuss a new toy model of "radially reduced" four-dimensional CDT in which we can take the continuum limit analytically and obtain a scale dependent spectral dimension varying from four to two with scale. Furthermore, the functional behaviour of the spectral dimension is exactly of the form which was conjectured on the basis of the numerical results.