Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral dimension of a quantum universe   In this paper, we calculate in a transparent way the spectral dimension of a
quantum spacetime, considering a diffusion process propagating on a fluctuating
manifold. To describe the erratic path of the diffusion, we implement a minimal
length by averaging the graininess of the quantum manifold in the flat space
case. As a result we obtain that, for large diffusion times, the quantum
spacetime behaves like a smooth differential manifold of discrete dimension. On
the other hand, for smaller diffusion times, the spacetime looks like a fractal
surface with a reduced effective dimension. For the specific case in which the
diffusion time has the size of the minimal length, the spacetime turns out to
have a spectral dimension equal to 2, suggesting a possible renormalizable
character of gravity in this regime. For smaller diffusion times, the spectral
dimension approaches zero, making any physical interpretation less reliable in
this extreme regime. We extend our result to the presence of a background field
and curvature. We show that in this case the spectral dimension has a more
complicated relation with the diffusion time, and conclusions about the
renormalizable character of gravity become less straightforward with respect to
what we found with the flat space analysis.

10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph