1202.2710 (Georgios Giasemidis et al.)

Dynamical dimensional reduction in toy models of 4D causal quantum
gravity    [PDF]

Georgios Giasemidis, John F. Wheater, Stefan Zohren

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) [Ambj{\o}rn et al., Phys. Rev. Lett. 95 (2005) 171]. 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 letter we propose 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.

View original: http://arxiv.org/abs/1202.2710