Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance

Abstract

We explore the nonperturbative renormalization group flow of Quantum Einstein Gravity (QEG) on an infinite dimensional theory space. We consider "conformally reduced" gravity where only fluctuations of the conformal factor are quantized and employ the Local Potential Approximation for its effective average action. The requirement of "background independence" in quantum gravity entails a partial differential equation governing the scale dependence of the potential for the conformal factor which differs significantly from that of a scalar matter field. In the infinite dimensional space of potential functions we find a Gaussian as well as a non-Gaussian fixed point which provides further evidence for the viability of the asymptotic safety scenario. The analog of the invariant cubic in the curvature which spoils perturbative renormalizability is seen to be unproblematic for the asymptotic safety of the conformally reduced theory. The scaling fields and dimensions of both fixed points are obtained explicitly and possible implications for the predictivity of the theory are discussed. Spacetime manifolds with $R^d$ as well as $S^d$ topology are considered. Solving the flow equation for the potential numerically we obtain examples of renormalization group trajectories inside the ultraviolet critical surface of the non-Gaussian fixed point. The quantum theories based upon some of them show a phase transition from the familiar (low energy) phase of gravity with spontaneously broken diffeomorphism invariance to a new phase of unbroken diffeomorphism invariance; the latter phase is characterized by a vanishing expectation value of the metric.

References in corpus (78)

• Exact evolution equation for the effective potential
• Background Independent Quantum Gravity: A Status Report
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Nonperturbative Evolution Equation for Quantum Gravity
• Aspects of the Functional Renormalisation Group
• Optimised Renormalisation Group Flows
• Renormalization group improved black hole spacetimes
• Optimisation of the exact renormalisation group
• Spectral Dimension of the Universe
• Fixed points of quantum gravity
• Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation
• Emergence of a 4D World from Causal Quantum Gravity
• Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
• Reconstructing the Universe
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Non-Trivial Ultraviolet Fixed Point in Quantum Gravity
• Galaxy Rotation Curves Without Non-Baryonic Dark Matter
• Fixed Points of Higher Derivative Gravity
• Fractal Spacetime Structure in Asymptotically Safe Gravity
• Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
• Ultraviolet properties of f(R)-Gravity
• The Asymptotic Safety Scenario in Quantum Gravity -- An Introduction
• The Running Gravitational Couplings
• On the renormalization group flow of f(R)-gravity
• Spacetime Structure of an Evaporating Black Hole in Quantum Gravity
• Asymptotic Safety of Gravity Coupled to Matter
• Is Quantum Einstein Gravity Nonperturbatively Renormalizable?
• Cosmology with Self-Adjusting Vacuum Energy Density from a Renormalization Group Fixed Point
• Contraints on Matter from Asymptotic Safety
• Renormalization group improved gravitational actions: a Brans-Dicke approach
• On Truncations of the Exact Renormalization Group
• Fixed points of quantum gravity in extra dimensions
• Mind The Gap
• The Universe from Scratch
• Quantum Gravity at Astrophysical Distances?
• Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves
• Galaxy Cluster Masses Without Non-Baryonic Dark Matter
• Gravitational Theory, Galaxy Rotation Curves and Cosmology without Dark Matter
• Proper Time Flow Equation for Gravity
• Quantum Gravity effects near the null black hole singularity
• Semiclassical Universe from First Principles
• From Big Bang to Asymptotic de Sitter: Complete Cosmologies in a Quantum Gravity Framework
• Background Independence and Asymptotic Safety in Conformally Reduced Gravity
• A class of nonlocal truncations in Quantum Einstein Gravity and its renormalization group behavior
• Entropy signature of the running cosmological constant
• Confronting the IR Fixed Point Cosmology with High Redshift Observations
• Quantum Gravity on the Lattice
• Towards Nonperturbative Renormalizability of Quantum Einstein Gravity
• Effective average action in statistical physics and quantum field theory
• Cosmological Perturbations in Renormalization Group Derived Cosmologies
• Functional Renormalization Group Equations, Asymptotic Safety, and Quantum Einstein Gravity
• Dimensionally reduced gravity theories are asymptotically safe
• Fixed-Point Structure of Scalar Fields
• On fixed points of quantum gravity
• A Minimal Length from the Cutoff Modes in Asymptotically Safe Quantum Gravity
• On the Gravitational Scaling Dimensions
• Signatures of gravitational fixed points at the LHC
• On the Ultraviolet Behaviour of Newton's constant
• Renormalization and asymptotic safety in truncated quantum Einstein gravity
• On the Fixed-Point Structure of Scalar Fields
• Nonlocal Quantum Gravity and the Size of the Universe
• Scale-dependent metric and causal structures in Quantum Einstein Gravity
• Arnowitt-Deser-Misner gravity with variable G and Lambda and fixed point cosmologies from the renormalization group
• Renormalization of the Topological Charge in Yang-Mills Theory
• Non-Trivial Directions for Scalar Fields
• Fixed points of quantum gravity in higher dimensions
• Effective Average Action of Chern-Simons Field Theory
• A Class of Renormalization Group Invariant Scalar Field Cosmologies
• Average Effective Potential for the Conformal Factor
• Quantum Relaxation of the Cosmological Constant
• String theory as a universal language
• Rotation Symmetry Breaking Condensate in a Scalar Theory
• Effective Potential of the Conformal Factor: Gravitational Average Action and Dynamical Triangulations
• The Accelerated expansion of the Universe as a crossover phenomenon
• Modified Dispersion Relations from the Renormalization Group of Gravity
• Noether symmetry approach in pure gravity with variable G and Lambda
• Flow equation for Halpern-Huang directions of scalar O(N) models
• Non-perturbative scaling in the scalar theory

Cited by in corpus (67)

• The nonperturbative functional renormalization group and its applications
• Quantum Einstein Gravity
• Taming perturbative divergences in asymptotically safe gravity
• Renormalisation group and the Planck scale
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Renormalization Group Flow in Scalar-Tensor Theories. I
• Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety
• En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Light fermions in quantum gravity
• Resolving Spacetime Singularities within Asymptotic Safety
• Matter Induced Bimetric Actions for Gravity
• Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity
• Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario
• Viability of quantum-gravity induced ultraviolet completions for matter
• Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity
• Asymptotic safety in an interacting system of gravity and scalar matter
• Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
• On unimodular quantum gravity
• The Renormalization Group and Weyl-invariance
• Effective universality in quantum gravity
• Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
• Conformally reduced quantum gravity revisited
• Fixed-Functionals of three-dimensional Quantum Einstein Gravity
• Graviton fluctuations erase the cosmological constant
• The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
• Large curvature and background scale independence in single-metric approximations to asymptotic safety
• Renormalization Group Flow in Scalar-Tensor Theories. II
• Asymptotic Safety, Fractals, and Cosmology
• Running boundary actions, Asymptotic Safety, and black hole thermodynamics
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Asymptotic Safety, Emergence and Minimal Length
• Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
• Gravity with more or less gauging
• Faddeev-Popov ghosts in quantum gravity beyond perturbation theory
• Asymptotic safety goes on shell
• RG flow of Weyl-invariant dilaton gravity
• Fixed point structure of the conformal factor field in quantum gravity
• Infinite order quantum-gravitational correlations
• Asymptotically Safe $f(R)$-Gravity Coupled to Matter II: Global Solutions
• Scalar-Tensor theories within Asymptotic Safety
• Asymptotic safety and the cosmological constant
• Composite Operators in Asymptotic Safety
• Manifestly diffeomorphism invariant classical Exact Renormalization Group
• The unitary conformal field theory behind 2D Asymptotic Safety
• Modulated Ground State of Gravity Theories with Stabilized Conformal Factor
• Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
• Effective Potential of the Conformal Factor: Gravitational Average Action and Dynamical Triangulations
• Universality and symmetry breaking in conformally reduced quantum gravity
• Split Weyl transformations in quantum gravity
• Infrared limit of quantum gravity
• Lessons from conformally reduced quantum gravity
• The fate of non-polynomial interactions in scalar field theory
• Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
• Geometric operators in the asymptotic safety scenario for quantum gravity
• Evolution of cosmological perturbations in an RG-driven inflationary scenario
• On the scaling of composite operators in Asymptotic Safety
• Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity
• On the ultraviolet behavior of conformally reduced quadratic gravity
• Bare vs. Effective Fixed Point Action in Asymptotic Safety: The Reconstruction Problem
• RG flows of Quantum Einstein Gravity in the linear-geometric approximation
• The Effective Potential of the Conformal Factor in Asymptotically Safe Quantum Gravity
• On the Lorentz symmetry in conformally reduced Quantum Gravity
• Thermal RG Flow of AS Quantum Gravity
• Gravity models with nonlinear symmetry realization
• Higher-derivative four-dimensional sine-Gordon model
• Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity