1209.4376 (Gianluca Calcagni)

Multi-fractional spacetimes, asymptotic safety and Hořava-Lifshitz
gravity    [PDF]

Gianluca Calcagni

We compare the recently formulated multi-fractional spacetimes with field theories of quantum gravity based on the renormalization group (RG), such as asymptotic safety and Ho\v{r}ava-Lifshitz gravity. The change of spacetime dimensionality with the probed scale is realized in both cases by an adaptation of the measurement tools (`rods') to the scale, but in different ways. In the multi-fractional case, by an adaptation of the position-space measure, roughly corresponding to a scale dependence of the coordinates. In the case of RG-based theories, by an adaptation of the momenta. The two pictures are mapped into each other, thus presenting the fractal structure of spacetime in RG-based theories under an alternative perspective.

View original: http://arxiv.org/abs/1209.4376