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 str...

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Bibliographic Details
Published in:Universe (Basel) 2021-05, Vol.7 (5), p.125
Main Authors: Ferrero, Renata, Reuter, Martin
Format: Article
Language:English
Subjects:
asymptotic safety
functional renormalization group
geometric flows
Geometry
Gravity
Quantum field theory
quantum gravity
scale-spacetime
Spacetime
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Summary: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-spacetime” 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 that “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.
ISSN:2218-1997
2218-1997
DOI:10.3390/universe7050125