Random versus holographic fluctuations of the background metric. I. (Cosmological) running of space-time dimension

Understand

A profound quantum-gravitational effect of space-time dimension running with respect to the size of space-time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation [hep-th/0505113] as well as in renormalization group approach to quantum gravity [hep-th/0508202].

• Unfortunately, along these approaches the interpretation and the physical meaning of the effective change of dimension at shorter scales is not clear.
• The aim of this paper is twofold.
• First, we find that box-counting dimension in face of finite resolution of space-time (generally implied by quantum gravity) shows a simple way how both the qualitative and the quantitative features of this effect can be understood.