Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety

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.

References in corpus (10)

• Exact evolution equation for the effective potential
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
• Matter Induced Bimetric Actions for Gravity
• Background Independence and Asymptotic Safety in Conformally Reduced Gravity
• The Status of Modern Five-Dimensional Gravity
• Towards a $C$-function in 4D quantum gravity
• Background Independent Field Quantization with Sequences of Gravity-Coupled Approximants
• On the geometry of the theory space in the ERG formalism
• Dynamical diffeomorphisms

Cited by in corpus (5)

• Scalar-Tensor theories within Asymptotic Safety
• Is Lattice Quantum Gravity Asymptotically Safe? Making contact between Causal Dynamical Triangulations and the Functional Renormalization Group
• On the possibility of a novel (A)dS/CFT relationship emerging in Asymptotic Safety
• Phenomenological footprints of Lambda varying gravity theories inspired from quantum gravity models in the multi-messenger era
• Combinatorial Spacetime from Loop Quantum Gravity