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arXiv · 2103.15709

Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety

Renata Ferrero·Martin Reuter
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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-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.

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Renata Ferrero, Martin Reuter. 2021-03-29. Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety. https://doi.org/10.3390/universe7050125

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