Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards a Geometrization of Renormalization Group Histories in
  Asymptotic Safety   Considering the scale dependent effective spacetimes implied by the
functional renormalization group in d-dimensional Quantum Einstein Gravity, we
discuss the representation of entire evolution histories by means of a single,
(d + 1)-dimensional manifold furnished with a fixed (pseudo-) Riemannian
structure. This "scale-space-time" carries a natural foliation whose leaves are
the ordinary spacetimes seen at a given resolution. We propose a universal form
of the higher dimensional metric and discuss its properties. We show that,
under precise conditions, this metric is always Ricci flat and admits a
homothetic Killing vector field; if the evolving spacetimes are maximally
symmetric, their (d + 1)-dimensional representative has a vanishing Riemann
tensor even. The non-degeneracy of the higher dimensional metric which
"geometrizes" a given RG trajectory is linked to a monotonicity requirement for
the running of the cosmological constant, which we test in the case of
Asymptotic Safety.

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex