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.

24 pages, 6 figures; journal version with updated references

References in corpus (30)

• Exact evolution equation for the effective potential
• Asymptotic safety in higher-derivative gravity
• Fixed Points of Higher Derivative Gravity
• Ultraviolet properties of f(R)-Gravity
• Chiral symmetry breaking in continuum QCD
• On the renormalization group flow of f(R)-gravity
• Asymptotic safety guaranteed
• Asymptotically Safe Lorentzian Gravity
• xPert: Computer algebra for metric perturbation theory
• Fixed points of quantum gravity in extra dimensions
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Asymptotic safety in the f(R) approximation
• Search of scaling solutions in scalar-tensor gravity
• The Renormalization Group flow of unimodular f(R) gravity
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• 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
• Matter Induced Bimetric Actions for Gravity
• Quantum gravity and Standard-Model-like fermions
• Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity
• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
• Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
• Graviton fluctuations erase the cosmological constant
• Large curvature and background scale independence in single-metric approximations to asymptotic safety
• Background independent exact renormalization group for conformally reduced gravity
• The background scale Ward identity in quantum gravity
• Asymptotically Safe Grand Unification
• Composite Operators in Asymptotic Safety
• Covariant and background independent functional RG flow for the effective average action
• Error estimates and specification parameters for functional renormalization

Cited by in corpus (87)

• The nonperturbative functional renormalization group and its applications
• One force to rule them all: asymptotic safety of gravity with matter
• A Critique of the Asymptotic Safety Program
• Resolving Spacetime Singularities within Asymptotic Safety
• Aspects of asymptotic safety for quantum gravity
• Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox
• Quantum gravity: a fluctuating point of view
• Upper bound on the Abelian gauge coupling from asymptotic safety
• Dynamical renormalization of black-hole spacetimes
• Mass difference for charged quarks from asymptotically safe quantum gravity
• How perturbative is quantum gravity?
• Higgs scalar potential in asymptotically safe quantum gravity
• Effective universality in quantum gravity
• Zooming in on fermions and quantum gravity
• Finite Quantum Gravity Amplitudes -- no strings attached
• Dark Matter meets Quantum Gravity
• Variable Planck mass from the gauge invariant flow equation
• Quantum Improved Schwarzschild-(A)dS and Kerr-(A)dS Space-times
• Graviton fluctuations erase the cosmological constant
• Asymptotic safety and field parametrization dependence in the f(R) truncation
• Constraining power of asymptotic safety for scalar fields
• $d=4$ as the critical dimensionality of asymptotically safe interactions
• Lorentz invariance violations in the interplay of quantum gravity with matter
• Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity
• Finite temperature spectral functions in the O(N)-model
• Lorentz symmetry is relevant
• Asymptotic solutions in asymptotic safety
• Quantum-gravity predictions for the fine-structure constant
• Essential Quantum Einstein Gravity
• Light charged fermions in quantum gravity
• Asymptotic safety, string theory and the weak gravity conjecture
• Safety in darkness: Higgs portal to simple Yukawa systems
• The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking
• A link that matters: Towards phenomenological tests of unimodular asymptotic safety
• On the impact of Majorana masses in gravity-matter systems
• Infinite order quantum-gravitational correlations
• Scalar-Tensor theories within Asymptotic Safety
• Asymptotically Safe Gravity with Fermions
• DoFun 3.0: Functional equations in Mathematica
• Graviton-Mediated Scattering Amplitudes from the Quantum Effective Action
• Predictive power of grand unification from quantum gravity
• Scalegenesis and fermionic dark matters in the flatland scenario
• The weak-gravity bound in asymptotically safe gravity-gauge systems
• Black Holes in Asymptotically Safe Gravity
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Asymptotic freedom and safety in quantum gravity
• Exploring new corners of asymptotically safe unimodular quantum gravity
• Infrared limit of quantum gravity
• Is scale-invariance in gauge-Yukawa systems compatible with the graviton?
• Lessons from conformally reduced quantum gravity
• Pregeometry and spontaneous time-space asymmetry
• Are there ALPs in the asymptotically safe landscape?
• Momentum dependence of quantum critical Dirac systems
• Gravitational instantons and anomalous chiral symmetry breaking
• A curvature bound from gravitational catalysis in thermal backgrounds
• Nonvanishing gravitational contribution to matter beta functions for vanishing dimensionful regulators
• On the weak-gravity bound for a shift-symmetric scalar field
• Background independent exact renormalisation
• On the scaling of composite operators in Asymptotic Safety
• Effective action and black hole solutions in asymptotically safe quantum gravity
• BRST invariant RG flows
• Four-quark scatterings in QCD II
• Cosmology from pregeometry
• Effective Action from the Functional Renormalization Group
• Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge
• Constraints on discrete global symmetries in quantum gravity
• Evidence for a novel shift-symmetric universality class from the functional renormalization group
• An asymptotically safe guide to quantum gravity and matter
• Perturbative Asymptotic Safety and Its Phenomenological Applications
• On characterizing the Quantum Geometry underlying Asymptotic Safety
• Reconstructing the graviton
• Asymptotic safety in the dark
• Steps towards Lorentzian quantum gravity with causal sets
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the Asymptotically Safe Standard Model
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Lectures in Quantum Gravity
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• Scaling solutions for asymptotically free quantum gravity
• Ruling out models of vector dark matter in asymptotically safe quantum gravity
• Towards a Higgs mass determination in asymptotically safe gravity with a dark portal
• Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories
• Asymptotic safety and quantum gravity amplitudes
• On the reconstruction problem in Quantum Gravity
• Indications against dynamical CPT symmetry restoration in quantum gravity
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds