Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety
Ferrero R, Reuter M (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 7
Pages Range: 125
Issue: 5
Abstract
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.
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Germany (DE)How to cite
APA:
Ferrero, R., & Reuter, M. (2021). Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety. Universe, 7, 125. https://doi.org/10.3390/universe7050125
MLA:
Ferrero, Renata, and Martin Reuter. "Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety." Universe 7 (2021): 125.
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