Towards apparent convergence in asymptotically safe quantum gravity

Abstract

The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in \cite{Christiansen:2012rx,Christiansen:2014raa}, and implemented in \cite{Christiansen:2015rva} for propagators and three-point functions. In the present work this expansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows. In terms of a covariant operator expansion the current approximation gives access to $\Lambda$, $R$, $R^2$ as well as $R_{\mu \nu }^2$ and higher derivative operators. We find a UV fixed point with three attractive and two repulsive directions, thus confirming previous studies on the relevance of the first three operators. In the infrared we find trajectories that correspond to classical general relativity and further show non-classical behaviour in some fluctuation couplings. We also find signatures for the apparent convergence of the systematic vertex expansion. This opens a promising path towards establishing asymptotically safe gravity in terms of apparent convergence.

arXiv comment24 pages, 6 figures; journal version with updated references

References in corpus (104)

• Exact evolution equation for the effective potential
• Nonperturbative Evolution Equation for Quantum Gravity
• The Exact Renormalisation Group and Approximate Solutions
• Aspects of the Functional Renormalisation Group
• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• Optimisation of the exact renormalisation group
• FORM version 4.0
• Fixed points of quantum gravity
• Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation
• Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
• On the infrared behavior of Landau gauge Yang-Mills theory
• Quantum Einstein Gravity
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Asymptotic safety in higher-derivative gravity
• Non-Trivial Ultraviolet Fixed Point in Quantum Gravity
• Introduction to the functional RG and applications to gauge theories
• Fixed Points of Higher Derivative Gravity
• Ultraviolet properties of f(R)-Gravity
• Chiral symmetry breaking in continuum QCD
• Matter matters in asymptotically safe quantum gravity
• The Running Gravitational Couplings
• On the renormalization group flow of f(R)-gravity
• Landau gauge Yang-Mills correlation functions
• Asymptotic safety guaranteed
• Asymptotically Safe Lorentzian Gravity
• Further evidence for asymptotic safety of quantum gravity
• xPert: Computer algebra for metric perturbation theory
• Contraints on Matter from Asymptotic Safety
• Renormalisation group and the Planck scale
• Fixed points of quantum gravity in extra dimensions
• Asymptotic safety of gravity-matter systems
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Renormalization Group Flow in Scalar-Tensor Theories. I
• Scaling Exponents in Quantum Gravity near Two Dimensions
• Local Quantum Gravity
• The Gravitational Two-Loop Counterterm is Asymptotically Safe
• QED coupled to QEG
• Asymptotic safety in the f(R) approximation
• Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety
• Search of scaling solutions in scalar-tensor gravity
• Global Flows in Quantum Gravity
• The Renormalization Group flow of unimodular f(R) gravity
• Asymptotic freedom of Yang-Mills theory with gravity
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• Quantum gravity on foliated spacetime - asymptotically safe and sound
• En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
• Proper Time Flow Equation for Gravity
• Generalized Parametrization Dependence in Quantum Gravity
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Light fermions in quantum gravity
• A flow equation for f(R) gravity and some of its exact solutions
• Spectral Functions for the Quark-Meson Model Phase Diagram from the Functional Renormalization Group
• Matter Induced Bimetric Actions for Gravity
• Quantum-gravity effects on a Higgs-Yukawa model
• Flow Equations for Yang-Mills Theories in General Axial Gauges
• Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario
• Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity
• Transport Coefficients in Yang--Mills Theory and QCD
• Real time correlation functions and the functional renormalisation group
• Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization
• Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity
• Asymptotic safety in $O(N)$ scalar models coupled to gravity
• Quantum gravity and Standard-Model-like fermions
• Higher Derivative Gravity and Asymptotic Safety in Diverse Dimensions
• Chiral fermions in asymptotically safe quantum gravity
• Consistent closure of renormalization group flow equations in quantum gravity
• The R^2 phase-diagram of QEG and its spectral dimension
• Renormalisation of Newton's constant
• Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity
• On the number of relevant operators in asymptotically safe gravity
• Dilaton Quantum Gravity
• Background independence in a background dependent renormalization group
• Functional renormalization with fermions and tetrads
• FormTracer - A Mathematica Tracing Package Using FORM
• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
• Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
• Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group
• Graviton fluctuations erase the cosmological constant
• Scaling solutions for Dilaton Quantum Gravity
• Large curvature and background scale independence in single-metric approximations to asymptotic safety
• Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
• Background independent exact renormalization group for conformally reduced gravity
• Theorems for Asymptotic Safety of Gauge Theories
• Analytic continuation of functional renormalization group equations
• Connections and geodesics in the space of metrics
• The background scale Ward identity in quantum gravity
• The Price of an Exact, Gauge-Invariant RG-Flow Equation
• Asymptotically Safe Grand Unification
• Non-perturbative QEG Corrections to the Yang-Mills Beta Function
• Composite Operators in Asymptotic Safety
• Asymptotic safety and the cosmological constant
• Essential nature of Newton's constant in unimodular gravity
• Manifestly diffeomorphism invariant classical Exact Renormalization Group
• CrasyDSE: A framework for solving Dyson-Schwinger equations
• Infrared fixed point in quantum Einstein gravity
• Splitting Ward identity
• Self-consistent Spectral Functions in the $O(N)$ Model from the FRG
• Quantum Critical Behaviour of Semi-Simple Gauge Theories
• Covariant and background independent functional RG flow for the effective average action
• Conformal Gauge-Yukawa Theories away From Four Dimensions
• Covariant and single-field effective action with the background-field formalism
• Asymptotically safe and free chiral theories with and without scalars
• Critical exponents in quantum Einstein gravity
• Error estimates and specification parameters for functional renormalization

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