On the possibility of a novel (A)dS/CFT relationship emerging in Asymptotic Safety

Abstract

Quantum Einstein Gravity (QEG), nonperturbatively renormalized by means of a certain asymptotically safe renormalization group (RG) trajectory, is explored by solving its scale dependent effective field equations and embedding the family of emerging 4-dimensional spacetimes into a single 5-dimensional manifold, which thus encodes the complete information about all scales. By construction the latter manifold is furnished with a natural foliation. Heuristically, its leaves are interpreted as physical spacetime observed on different scales of the experimental resolution. Generalizing earlier work on the embedding of $d$-dimensional Euclidean QEG spacetimes in $(d+1)$-dimensional flat or Ricci flat manifolds, we admit Lorentzian signature in this paper and we consider embeddings in arbitrary $(d+1)$-dimensional Einstein spaces. Special attention is paid to the sector of maximally symmetric metrics, and the fundamental definition of QEG in $d=4$ that employs the cross-over trajectory connecting the non-Gaussian to the Gaussian RG fixed point. Concerning the embedding of the resulting family of 4D de Sitter solutions with a running Hubble parameter, we find that there are only two possible 5D spacetimes, namely the anti-de Sitter manifold AdS${}_5$ and the de Sitter manifold dS${}_5$. To arrive at this result essential use is made of the monotone scale dependence of the running cosmological constant featured by the gravitational effective average action. We show that if the scale invariance of the QEG fixed points extends to full conformal invariance, the 5D picture of the resulting geometric and field theoretic structure displays a novel kind of "AdS/CFT correspondence". While strongly reminiscent of the usual string theory-based AdS/CFT correspondence, also clear differences are found.

arXiv comment47 pages, 10 figures; further remarks and explanations added, title changed

References in corpus (43)

• Gauge Theory Correlators from Non-Critical String Theory
• Exact evolution equation for the effective potential
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• The dS/CFT Correspondence
• Nonperturbative Evolution Equation for Quantum Gravity
• On the Holographic Renormalization Group
• Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation
• Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
• Holographic and Wilsonian Renormalization Groups
• How to go with an RG Flow
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Fractal Spacetime Structure in Asymptotically Safe Gravity
• The Running Gravitational Couplings
• Renormalization Flow of Bound States
• Is Quantum Einstein Gravity Nonperturbatively Renormalizable?
• A remark on the AdS/CFT correspondence and the renormalization group flow
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety
• The boundary S-matrix and the AdS to CFT dictionary
• En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
• Matter Induced Bimetric Actions for Gravity
• Non-perturbative unitarity and fictitious ghosts in quantum gravity
• Evolution Equations for the Quark-Meson Transition
• Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
• Renormalization Group Flow of the Holst Action
• Essential Quantum Einstein Gravity
• Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
• The "tetrad only" theory space: Nonperturbative renormalization flow and Asymptotic Safety
• Composite Operators in Asymptotic Safety
• The unitary conformal field theory behind 2D Asymptotic Safety
• Geometries with mismatched branes
• A note on scaling arguments in the effective average action formalism
• Towards a $C$-function in 4D quantum gravity
• Background Independent Field Quantization with Sequences of Gravity-Coupled Approximants
• A Holographic form for Wilson's RG
• A new functional flow equation for Einstein-Cartan quantum gravity
• Background Independent Field Quantization with Sequences of Gravity-Coupled Approximants II: Metric Fluctuations
• Probing crunching AdS cosmologies
• The Spectral Geometry of de Sitter Space in Asymptotic Safety
• Scale vs. Conformal Invariance at the IR Fixed Point of Quantum Gravity
• On selfdual spin-connections and Asymptotic Safety
• Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety
• Determining wave equations in holographic QCD from Wilsonian renormalization group

Cited by in corpus (1)

• Combinatorial Spacetime from Loop Quantum Gravity