Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox

Abstract

Over the last years the Asymptotic Safety program has matured into a serious candidate for a quantum theory of gravity compatible with observations. The rapid technical progress in computing renormalisation group flows for gravity and gravity-matter systems in the non-perturbative regime has put many interesting physical questions within reach. In particular, the construction of the non-perturbative quantum corrections to the propagation of fields on a fluctuating spacetime allows addressing the effective propagation of matter on a quantum spacetime or the possible resolution of spacetime singularities based on first principle computations. In this article, we assemble a technical toolbox for carrying out investigations on this promising research frontier. As a specific example we present results for the momentum-dependent two-point function for a scalar field induced by the quantum fluctuations of the underlying geometry in a self-consistent way.

48 pages, 2 Mathematica notebooks

References in corpus (127)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• General relativity as an effective field theory: The leading quantum corrections
• Nonperturbative Evolution Equation for Quantum Gravity
• Aspects of the Functional Renormalisation Group
• Quantum Einstein Gravity
• An Introduction to the Nonperturbative Renormalization Group
• Asymptotic safety in higher-derivative gravity
• Introduction to the functional RG and applications to gauge theories
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Ultraviolet properties of f(R)-Gravity
• Chiral symmetry breaking in continuum QCD
• Matter matters in asymptotically safe quantum gravity
• On the renormalization group flow of f(R)-gravity
• xTras: a field-theory inspired xAct package for Mathematica
• Asymptotic Safety of Gravity Coupled to Matter
• Further evidence for asymptotic safety of quantum gravity
• xPerm: fast index canonicalization for tensor computer algebra
• xPert: Computer algebra for metric perturbation theory
• Contraints on Matter from Asymptotic Safety
• Taming perturbative divergences in asymptotically safe gravity
• Asymptotic safety of gravity-matter systems
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Renormalization Group Flow in Scalar-Tensor Theories. I
• Local Quantum Gravity
• Scaling Exponents in Quantum Gravity near Two Dimensions
• QED coupled to QEG
• Asymptotic safety in the f(R) approximation
• Towards apparent convergence in asymptotically safe quantum gravity
• Top mass from asymptotic safety
• Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety
• Search of scaling solutions in scalar-tensor gravity
• Global Flows in Quantum Gravity
• One force to rule them all: asymptotic safety of gravity with matter
• Asymptotic freedom of Yang-Mills theory with gravity
• The Renormalization Group flow of unimodular f(R) gravity
• En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
• Asymptotic safety of quantum gravity beyond Ricci scalars
• Renormalization group fixed points of foliated gravity-matter systems
• Gravitational corrections to Yukawa systems
• Generalized Parametrization Dependence in Quantum Gravity
• Light fermions in quantum gravity
• Resolving Spacetime Singularities within Asymptotic Safety
• A flow equation for f(R) gravity and some of its exact solutions
• Lectures on renormalization and asymptotic safety
• An asymptotically safe solution to the U(1) triviality problem
• Matter Induced Bimetric Actions for Gravity
• Quantum-gravity effects on a Higgs-Yukawa model
• Running Gauge Coupling in Asymptotically Safe Quantum Gravity
• The Invar Tensor Package
• Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario
• Upper bound on the Abelian gauge coupling from asymptotic safety
• Curvature dependence of quantum gravity
• Quantum gravity fluctuations flatten the Planck-scale Higgs potential
• Viability of quantum-gravity induced ultraviolet completions for matter
• Wilsonian flows and background fields
• Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization
• A proper fixed functional for four-dimensional Quantum Einstein Gravity
• The local potential approximation in quantum gravity
• Asymptotic safety in $O(N)$ scalar models coupled to gravity
• Mass difference for charged quarks from asymptotically safe quantum gravity
• Asymptotic safety in an interacting system of gravity and scalar matter
• Quantum gravity and Standard-Model-like fermions
• Chiral fermions in asymptotically safe quantum gravity
• How perturbative is quantum gravity?
• Consistent closure of renormalization group flow equations in quantum gravity
• The Universal RG Machine
• Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
• Higgs scalar potential in asymptotically safe quantum gravity
• Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system
• Zooming in on fermions and quantum gravity
• Effective universality in quantum gravity
• Dilaton Quantum Gravity
• Renormalisation group flows for gauge theories in axial gauges
• Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
• The Heavy Quark Potential from Wilson's Exact Renormalization Group
• Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter
• Status of the asymptotic safety paradigm for quantum gravity and matter
• Correlation functions on a curved background
• Nonminimal hints for asymptotic safety
• Background independence in a background dependent renormalization group
• Functional renormalization with fermions and tetrads
• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
• Global solutions of functional fixed point equations via pseudo-spectral methods
• Variable Planck mass from the gauge invariant flow equation
• Graviton fluctuations erase the cosmological constant
• Asymptotic safety and field parametrization dependence in the f(R) truncation
• Scaling solutions for Dilaton Quantum Gravity
• Large curvature and background scale independence in single-metric approximations to asymptotic safety
• Background independent exact renormalization group for conformally reduced gravity
• EPFL Lectures on General Relativity as a Quantum Field Theory
• On the non-local heat kernel expansion
• Connections and geodesics in the space of metrics
• The background scale Ward identity in quantum gravity
• $d=4$ as the critical dimensionality of asymptotically safe interactions
• Solving functional flow equations with pseudo-spectral methods
• Solutions to the reconstruction problem in asymptotic safety
• Quantum-gravity predictions for the fine-structure constant
• Cosmological bounds on the field content of asymptotically safe gravity-matter models
• Fermions in gravity with local spin-base invariance
• On avoiding Ostrogradski instabilities within Asymptotic Safety
• The Planck scale, the Higgs mass and scalar dark matter
• On de Sitter solutions in asymptotically safe $f(R)$ theories
• Computing the Effective Action with the Functional Renormalization Group
• On the impact of Majorana masses in gravity-matter systems
• Infinite order quantum-gravitational correlations
• Two-loop Renormalization in Quantum Gravity near Two Dimensions
• Asymptotically Safe $f(R)$-Gravity Coupled to Matter II: Global Solutions
• Background Scale Independence in Quantum Gravity
• Manifestly diffeomorphism invariant classical Exact Renormalization Group
• Higher Derivative Gravity from the Universal Renormalization Group Machine
• The phase diagram of quantum gravity from diffeomorphism-invariant RG-flows
• Consistent early and late time cosmology from the RG flow of gravity
• The unitary conformal field theory behind 2D Asymptotic Safety
• Splitting Ward identity
• Geometrical effective action and Wilsonian flows
• Global surpluses of spin-base invariant fermions
• Split Weyl transformations in quantum gravity
• Is scale-invariance in gauge-Yukawa systems compatible with the graviton?
• Spin-base invariance of Fermions in arbitrary dimensions
• Covariant and background independent functional RG flow for the effective average action
• Can we see quantum gravity? Photons in the asymptotic-safety scenario
• Covariant and single-field effective action with the background-field formalism
• A Review of Leading Quantum Gravitational Corrections to Newtonian Gravity
• Reflection positivity in higher derivative scalar theories
• Conformal symmetry and the cosmological constant problem
• Scales and hierachies in asymptotically safe quantum gravity: a review

Cited by in corpus (67)

• The nonperturbative functional renormalization group and its applications
• A Critique of the Asymptotic Safety Program
• Resolving Spacetime Singularities within Asymptotic Safety
• Quantum gravity: a fluctuating point of view
• Quasinormal ringing of regular black holes in asymptotically safe gravity: the importance of overtones
• Quantum Gravitational Corrections to the Entropy of a Schwarzschild Black Hole
• Finite Quantum Gravity Amplitudes -- no strings attached
• Dark Matter meets Quantum Gravity
• From renormalization group flows to cosmology
• Essential Quantum Einstein Gravity
• Light charged fermions in quantum gravity
• The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking
• Sifting quantum black holes through the principle of least action
• Non-Gaussianities and tensor-to-scalar ratio in non-local $R^2$-like inflation
• Scalar-Tensor theories within Asymptotic Safety
• Asymptotic Safety: Swampland or Wonderland?
• Asymptotically Safe Gravity with Fermions
• Graviton-Mediated Scattering Amplitudes from the Quantum Effective Action
• String Tension between de Sitter vacua and Curvature Corrections
• Predictive power of grand unification from quantum gravity
• Black Holes in Asymptotically Safe Gravity
• The weak-gravity bound in asymptotically safe gravity-gauge systems
• Relational observables in Asymptotically safe gravity
• Formation and evaporation of quantum black holes from the decoupling mechanism in quantum gravity
• Exploring new corners of asymptotically safe unimodular quantum gravity
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Asymptotic freedom and safety in quantum gravity
• Form Factors in Quantum Gravity - contrasting non-local, ghost-free gravity and Asymptotic Safety
• Lessons from conformally reduced quantum gravity
• Stable three-dimensional (un)charged AdS gravastars in gravity's rainbow
• Are there ALPs in the asymptotically safe landscape?
• Scattering amplitudes in affine gravity
• 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
• Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge
• Effective Action from the Functional Renormalization Group
• Suppression of spacetime singularities in quantum gravity
• Constraints on discrete global symmetries in quantum gravity
• Traces of quantum gravitational correction at third-order curvature through the black hole shadow and particle deflection at the weak field limit
• The Fröhlich-Morchio-Strocchi mechanism and quantum gravity
• Evidence for a novel shift-symmetric universality class from the functional renormalization group
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• The search for the universality class of metric quantum gravity
• Reconstructing the graviton
• 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
• Black Hole Remnants from Dynamical Dimensional Reduction?
• Non-perturbative quantum Galileon in the exact renormalization group
• Scaling solutions for asymptotically free quantum gravity
• Ruling out models of vector dark matter in asymptotically safe quantum gravity
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories
• Quantum corrected gravitational potential beyond monopole-monopole interactions
• Asymptotic safety and quantum gravity amplitudes
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
• Stability of the de-Sitter universe: One-loop nonlocal $f(R)$ gravity
• Indications against dynamical CPT symmetry restoration in quantum gravity
• On the reconstruction problem in Quantum Gravity
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds
• De Sitter scattering amplitudes in the Born approximation
• The stability of the de-Sitter universe in nonlocal gravity
• Charting GLOBs in Asymptotically Safe Gravity