Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity

Abstract

Investigations of Quantum Einstein Gravity (QEG) based upon the effective average action employ a flow equation which does not contain any ultraviolet (UV) regulator. Its renormalization group trajectories emanating from a non-Gaussian fixed point define asymptotically safe quantum field theories. A priori these theories are, somewhat unusually, given in terms of their effective rather than bare action. In this paper we construct a functional integral representation of these theories. We fix a regularized measure and show that every trajectory of effective average actions, depending on an IR cutoff only, induces an associated trajectory of bare actions which depend on a UV cutoff. Together with the regularized measure these bare actions give rise to a functional integral which reproduces the prescribed effective action when the UV cutoff is removed. In this way we are able to reconstruct the underlying microscopic ("classical") system and identify its fundamental degrees of freedom and interactions. The bare action of the Einstein-Hilbert truncation is computed and its flow is analyzed as an example. Various conceptual issues related to the completion of the asymptotic safety program are discussed.

44 pages. Minor corrections. Accepted for publication in Phys.Rev.D

References in corpus (73)

• 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
• Fixed points of quantum gravity in extra dimensions
• Mind The Gap
• Discrete structures in gravity
• 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
• 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
• Renormalizability of gauge theories in extra dimensions
• 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
• Towards Nonperturbative Renormalizability of Quantum Einstein Gravity
• Cosmic Microwave Background, Accelerating Universe and Inhomogeneous Cosmology
• Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance
• Effective average action in statistical physics and quantum field theory
• Functional Renormalization Group Equations, Asymptotic Safety, and Quantum Einstein Gravity
• Cosmological Perturbations in Renormalization Group Derived Cosmologies
• Dimensionally reduced gravity theories are asymptotically safe
• 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
• Fixed Points of Nonlinear Sigma Models in d>2
• On the Ultraviolet Behaviour of Newton's constant
• Renormalization and asymptotic safety in truncated quantum Einstein gravity
• Nonlocal Quantum Gravity and the Size of the Universe
• Hamiltonian and physical Hilbert space in polymer quantum mechanics
• 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
• Fixed points of quantum gravity in higher dimensions
• A Class of Renormalization Group Invariant Scalar Field Cosmologies
• Quantum Liouville Field Theory as Solution of a Flow Equation
• 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
• Loop quantization as a continuum limit
• Discrete and Continuum Quantum Gravity

Cited by in corpus (50)

• The nonperturbative functional renormalization group and its applications
• Quantum Einstein Gravity
• Asymptotic safety in higher-derivative 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
• Black holes within Asymptotic Safety
• Matter Induced Bimetric Actions for Gravity
• Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox
• Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity
• Einstein-Cartan wormhole solutions
• Status of the asymptotic safety paradigm for quantum gravity and matter
• Conformally reduced quantum gravity revisited
• Renormalization Group Flow in Scalar-Tensor Theories. II
• Asymptotic Safety, Fractals, and Cosmology
• Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
• On the physical mechanism underlying Asymptotic Safety
• Faddeev-Popov ghosts in quantum gravity beyond perturbation theory
• Polyakov Effective Action from Functional Renormalization Group Equation
• Computing the Effective Action with the Functional Renormalization Group
• Infinite order quantum-gravitational correlations
• Scalar-Tensor theories within Asymptotic Safety
• Composite Operators in Asymptotic Safety
• The unitary conformal field theory behind 2D Asymptotic Safety
• Higgs inflation and quantum gravity: An exact renormalisation group approach
• Formation and evaporation of quantum black holes from the decoupling mechanism in quantum gravity
• Form Factors in Quantum Gravity - contrasting non-local, ghost-free gravity and Asymptotic Safety
• Functional renormalization group of the non-linear sigma model and the O(N) universality class
• Trace anomaly and infrared cutoffs
• Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
• Scalar-Tensor gravity with system-dependent potential and its relation with Renormalization Group extended General Relativity
• BRST invariant RG flows
• The Spectral Geometry of de Sitter Space in Asymptotic Safety
• Functional RG flow equation: regularization and coarse-graining in phase space
• Existence and Construction of Exact FRG Flows of a UV-Interacting Scalar Field Theory
• Running Immirzi Parameter and Asymptotic Safety
• On quantum gravity, Asymptotic Safety, and paramagnetic dominance
• Lectures in Quantum Gravity
• Bare vs. Effective Fixed Point Action in Asymptotic Safety: The Reconstruction Problem
• On the possibility of a novel (A)dS/CFT relationship emerging in Asymptotic Safety
• RG flows of Quantum Einstein Gravity in the linear-geometric approximation
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• On the reconstruction problem in Quantum Gravity
• Are there any Landau poles in wavelet-based quantum field theory?
• Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity