Nonperturbative Evolution Equation for Quantum Gravity

Abstract

A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies modified BRS Ward--Identities. The evolution equation is solved for a simple truncation of the space of actions. In 2+epsilon dimensions, nonperturbative corrections to the beta--function of Newton's constant are derived and its dependence on the cosmological constant is investigated. In 4 dimensions, Einstein gravity is found to be ``antiscreening'', i.e., Newton's constant increases at large distances.

35 pages, latex

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• Spherically symmetric ADM gravity with variable G and Lambda(c)
• Large "Dipolar" Vacuum Fluctuations in Quantum Gravity
• Linking the trans-Planckian and the information loss problems in black hole physics
• Primordial flat frame -- a new view on inflation
• Quantum Cosmology and the Inflationary Spectra from a Non-Minimally Coupled Inflaton
• Critical Phenomena in Causal Dynamical Triangulations
• Dynamically emergent gravity from hidden local Lorentz symmetry
• Relationships Between Exact RGs and some Comments on Asymptotic Safety
• Inverse logarithmic correction in the HBAR entropy of an atom falling into a renormalization group improved charged black hole
• Not so non-renormalizable gravity
• Dilution of zero point energies in the cosmological expansion
• Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space
• Gravitational Collapse in Scale-Dependent Gravity
• Conformal anomaly from gauge fields without gauge fixing
• Scalar fields in Causal Dynamical Triangulations
• Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories
• The effects of running gravitational coupling on three dimensional black holes
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• Foliation-based approach to quantum gravity and applications to astrophysics
• Five-dimensional scale-dependent black holes with constant curvature and Solv horizons
• Generalized Ellis-Bronnikov wormholes in asymptotically safe gravity
• Gauge Invariant Cutoff QED
• Reduction of gravity-matter and dS gravity to hypersurface
• Entropic force, running gravitational coupling and future singularities
• Spectral Methods and Running Scales in Causal Dynamical Triangulations
• Heat kernel coefficients for massive gravity
• Cosmology of Bianchi type-I metric using renormalization group approach for quantum gravity
• Vacuum properties of nonsymmetric gravity in de Sitter space
• Scale Dependent Metric and Minimal Length in QEG
• $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the Asymptotically Safe Standard Model
• 4D covariance of holographic quantization of Einstein gravity
• Evaporating loop quantum black hole
• A matter-dominated cosmological model with variable $G$ and $\Lambda$. Confrontation of theoretical predictions with observational data
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Lorentz-violating dynamics in the pre-Planckian Universe
• Gravitational Fluctuations as an Alternative to Inflation
• On the ultraviolet behavior of conformally reduced quadratic gravity
• On the interior of (Quantum) Black Holes
• QFT without infinities and hierarchy problem
• Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety
• Gravitational renormalization of quantum field theory
• Regular black holes with improved energy conditions and their analogues in fluids
• Properties of dynamical fractal geometries in the model of Causal Dynamical Triangulations
• Background independence and field redefinitions in quantum gravity
• Asymptotic safety in the sine-Gordon model
• Quantum gravity in timeless configuration space
• Some comments on the universal constant in DSR
• Irreversible vierbein postulate: Emergence of spacetime from quantum phase transition
• Effective scalar potential in asymptotically safe quantum gravity
• Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
• A Lorentzian renormalisation group equation for gauge theories
• The continuum limit of quantum gravity at second order in perturbation theory
• Parisi-Sourlas-like dimensional reduction of quantum gravity in the presence of observers
• Nonthermal radiation of evaporating black holes
• Black hole evaporation within a momentum-dependent metric
• Scaling solution for field-dependent gauge couplings in quantum gravity
• Space of non-Fermi liquids
• $\mathcal{N}=2$ supersymmetry and anisotropic scale invariance
• Dark side of Weyl gravity
• Revisit of renormalization of Einstein-Maxwell theory at one-loop
• Interference and reflection from the event horizon of a quantum corrected black hole
• On quantum gravity, Asymptotic Safety, and paramagnetic dominance
• A technique for natural gauge boson masses
• The Possibility of Inflation in Asymptotically Safe Gravity
• Stringballs and Planckballs for Dark Matter
• Black hole thermodynamics in asymptotically safe gravity
• Time Variable Cosmological Constant from Renormalization Group Equations
• Bare vs. Effective Fixed Point Action in Asymptotic Safety: The Reconstruction Problem
• Regular black hole from a confined spin connection in Poincare gauge gravity
• Image of Quantum Improved Regular Kerr Black Hole and Parameter Constraints from EHT Observations
• Lectures in Quantum Gravity
• Asymptotically Safe Hilbert-Palatini Gravity in an On-Shell Reduction Scheme
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• Renormalization of lattice-regularized quantum gravity models I. General considerations
• Hints of (trans-Planckian) asymptotic freedom in semiclassical cosmology
• Running of the Cosmological Constant and Estimate of its Value in Quantum General Relativity
• On the effect of renormalization group improvement on the cosmological power spectrum
• Casimir effect: running Newton constant or cosmological term
• Einstein-Heisenberg Consistency Condition Interplay with Cosmological Constant Prediction in Resummed Quantum Gravity
• On the landscape of scale invariance in quantum mechanics
• Quantum gravity and gravitational-wave astronomy
• The local potential approximation in the background field formalism
• Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models
• Renormalization of Einstein gravity through a derivative-dependent field redefinition
• Properties of a proposed background independent exact renormalization group
• Functional RG flow of the effective Hamiltonian action
• Spinor gravity and diffeomorphism invariance on the lattice
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• The continuum limit of the conformal sector at second order in perturbation theory
• Phonon renormalization and Pomeranchuk instability in the Holstein model
• A new functional RG flow: regulator-sourced 2PI versus average 1PI
• On the possibility of a novel (A)dS/CFT relationship emerging in Asymptotic Safety
• Scaling solutions for asymptotically free quantum gravity
• Vacuum energy, the Casimir effect, and Newton's non-constant
• Suppression of proton decay in quantum gravity
• Ruling out models of vector dark matter in asymptotically safe quantum gravity
• Black hole dynamical evolution in a Lorentz-violating spacetime
• Variable $G$ and $\Lambda$ gravity theory and analytical Cosmological Solutions using Noether symmetry approach
• Spectral Analysis of Quasinormal Modes of Planck Stars
• Time Evolution and Thermal Renormalization Group Flow in Cosmology
• Towards a Higgs mass determination in asymptotically safe gravity with a dark portal
• The UV behavior of Gravity at Large N
• Quantum gravity: unification of principles and interactions, and promises of spectral geometry
• Noether symmetry approach to scalar-field-dominated cosmology with dynamically evolving G and Lambda
• Renormalization Group-Improved Gravitational Action: A Lagrangian Framework
• Lectures on Naturalness, String Landscape and Multiverse
• Aspects of quantum gravity
• Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum
• Regulator dependence of fixed points in quantum Einstein gravity with $R^2$ truncation
• Weak Lensing, Shear and the Cosmic Virial Theorem in a Model with a Scale-Dependent Gravitational Coupling
• Quantum corrected gravitational potential beyond monopole-monopole interactions
• Gravitational renormalization of quantum field theory: a "conservative" approach
• Black holes in asymptotic safety with higher derivatives: accretion and stability analysis
• Semi-classical locality for the non-relativistic path integral in configuration space
• Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories
• Vacuum Energy and Renormalization of the Field-Independent Term
• Stabilizing dark matter with quantum scale symmetry
• Constraining the swiss-cheese IR-fixed point cosmology with cosmic expansion
• Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff-Sagnotti counter-terms, and geometric flows
• What happens to topological invariants (and black holes) in singularity-free theories?
• Prediction for the Cosmological Constant and Constraints on Susy GUTS in Resummed Quantum Gravity
• Geometry-Information Duality: Quantum Entanglement Contributions to Gravitational Dynamics
• Preferred foliation effects in Quantum General Relativity
• On the quantum gravastar
• Dynamical analysis and cosmological viability of varying $G$ and $\Lambda$ cosmology
• On the Lorentz symmetry in conformally reduced Quantum Gravity
• Asymptotic safety and quantum gravity amplitudes
• Constraints on the Scale Parameter of Regular Black Hole in Asymptotically Safe Gravity from Extreme Mass Ratio Inspirals
• Commutative deformations of general relativity: nonlocality, causality, and dark matter
• Functional Renormalization Group Flow of Massive Gravity
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Scalar-QED β-functions near Planck's Scale
• Tensors and Algebras: An Algebraic Spacetime Interpretation for Tensor Models
• Phenomenological footprints of Lambda varying gravity theories inspired from quantum gravity models in the multi-messenger era
• Regular Black Hole Cores via Gravitational Evanescence of Collapsing Matter
• Quantum harmonic oscillator in a time dependent noncommutative background
• From negative to positive cosmological constant through decreasing temperature of the Universe: connection with string theory and spacetime foliation results
• Asymptotically free and safe quantum gravity scenarios consistent with Hubble, laboratory, and inflation scale physics
• A Universe from a Lagrangian Fixed Point
• Reformulations of Yang-Mills Theories with Space-time Tensor Fields
• A construction principle for ADM-type theories in maximal slicing gauge
• Non-renormalizable theories and finite formulation of QFT
• Quantum Field Theory on Multifractal Spacetime: Varying Dimension and Ultraviolet Completeness
• From minimal-length quantum theory to modified gravity
• Investigating the role of mutual information in the Page curve for a functional renormalization group improved Schwarzschild black hole
• Image of a quantum-corrected black hole without Cauchy horizons illuminated by a static thin accretion disk
• Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation
• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces
• Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams
• Infrared behavior of Weyl Gravity
• Functional Renormalization Group Analysis of $O(3)$ Nonlinear Sigma Model and Non-Abelian Bosonization Duality
• Scale-invariant random geometry from mating of trees: a numerical study
• Physics-informed operator flows and observables
• Scale-dependent gravity and covariant scale-setting
• Thermal RG Flow of AS Quantum Gravity
• IR-Improved Amplitude-Based Resummation in Quantum Field Theory: New Results and New Issues
• Local(ish) gravity theories in conformal superspace
• Functional-renormalization-group approach to strongly coupled Bose-Fermi mixtures in two dimensions
• On the reconstruction problem in Quantum Gravity
• Indications against dynamical CPT symmetry restoration in quantum gravity
• Shadow of rotating black holes with consistent thermodynamics
• Weyl-Invariant Quantization of Liouville Field Theory
• Effective quantum gravity observables and locally covariant QFT
• Vertex functions and their flow equations from the 2PI effective action
• Invariant Renormalization-Group improvement
• Quantum Gravity models - brief conceptual summary
• Averaging procedure in variable-G cosmologies
• Charting GLOBs in Asymptotically Safe Gravity
• A Information-Theoretic View on Spacetime
• Some Aspects of the Canonical Analysis of Reuter-Weyer RG Improved Einstein-Hilbert Action
• Perturbative Renormalisation Group Improved Black Hole Solution and its Quasinormal Modes
• Functional Renormalization Analytically Continued
• New Approach to GUTs
• Are there any Landau poles in wavelet-based quantum field theory?
• Quasinormal modes of Bonanno-Reuter black holes via the Spectral Method
• Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape
• Renormalisation Group for Gravity and Dimensional Reduction
• Decay of uniformly rotating particles
• Cosmology from a gauge induced gravity
• Non-singular Bounce from a Phase transition
• Shadows of naked singularities and superspinars related to the revisited Kerr-de Sitter spacetimes
• Benchmarking regulator-sourced 2PI and average 1PI flow equations in zero dimensions
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds
• Basic properties of an alternative flow equation in gravity theories
• Higher-derivative four-dimensional sine-Gordon model
• Holographic beta function in de Sitter space
• Nonlocality in Quantum Gravity and the Breakdown of Effective Field Theory
• Asymptotic Safety and the Cosmic Coincidence Problem
• Renormalization group approaches to Quantum Gravity and Tensions in Modern Cosmology
• Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity
• A quantum theory of gravity
• Non-linear sigma models on constant curvature target manifolds: a functional renormalization group approach
• On the Quantum Improved Affine Gravity
• Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence
• De Sitter scattering amplitudes in the Born approximation
• Prediction for the Cosmological Constant in Resummed Quantum Gravity and Constraints on SUSY GUT's
• Spacetime discreteness via consistent microscopic measurement