Geometric operators in the asymptotic safety scenario for quantum gravity

Abstract

We consider geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gravity. We discuss the role of these operators from the Asymptotic Safety perspective, and compute their anomalous dimensions within the Einstein-Hilbert truncation. We also discuss certain subtleties arising in the definition of such geometric operators. Our results hint to an effective dimensional reduction of the considered geometric operators.

arXiv comment31 pages

References in corpus (73)

• 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
• Optimised Renormalisation Group Flows
• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• Nonperturbative Quantum Gravity
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Asymptotic safety in higher-derivative gravity
• Flow Equations for N Point Functions and Bound States
• Fractal Spacetime Structure in Asymptotically Safe Gravity
• Ultraviolet properties of f(R)-Gravity
• Matter matters in asymptotically safe quantum gravity
• The Running Gravitational Couplings
• Asymptotically Safe Lorentzian Gravity
• Further evidence for asymptotic safety of quantum gravity
• Contraints on Matter from Asymptotic Safety
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Local Quantum Gravity
• The Gravitational Two-Loop Counterterm is Asymptotically Safe
• Asymptotic safety in the f(R) approximation
• Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety
• Global Flows in Quantum Gravity
• One force to rule them all: asymptotic safety of gravity with matter
• 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
• Asymptotic safety of quantum gravity beyond Ricci scalars
• Renormalization group fixed points of foliated gravity-matter systems
• Dimension and Dimensional Reduction in Quantum Gravity
• A flow equation for f(R) gravity and some of its exact solutions
• Matter Induced Bimetric Actions for Gravity
• A class of nonlocal truncations in Quantum Einstein Gravity and its renormalization group behavior
• Curvature dependence of quantum gravity
• Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization
• Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data
• A proper fixed functional for four-dimensional Quantum Einstein Gravity
• The local potential approximation in quantum gravity
• Higher Derivative Gravity and Asymptotic Safety in Diverse Dimensions
• 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
• The R^2 phase-diagram of QEG and its spectral dimension
• Probing the quantum nature of spacetime by diffusion
• Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance
• Realization of symmetry in the ERG approach to quantum field theory
• On the number of relevant operators in asymptotically safe gravity
• Effective universality in quantum gravity
• A functional renormalization group equation for foliated spacetimes
• Correlation functions on a curved background
• Background independence in a background dependent renormalization group
• Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
• Fixed-Functionals of three-dimensional Quantum Einstein Gravity
• Asymptotic safety and field parametrization dependence in the f(R) truncation
• RG flows of Quantum Einstein Gravity on maximally symmetric spaces
• Impact of topology in foliated Quantum Einstein Gravity
• Renormalization Group Flow of the Holst Action
• Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
• Quantum gravity with torsion and non-metricity
• On de Sitter solutions in asymptotically safe $f(R)$ theories
• Fixed point structure of the conformal factor field in quantum gravity
• Infinite order quantum-gravitational correlations
• Composite Operators in Asymptotic Safety
• Quantum Liouville Field Theory as Solution of a Flow Equation
• A note on scaling arguments in the effective average action formalism
• Towards a $C$-function in 4D quantum gravity
• Quantization and fixed points of non-integrable Weyl theory
• Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
• Off-diagonal heat-kernel expansion and its application to fields with differential constraints
• Products of composite operators in the exact renormalization group formalism
• Scaling and Renormalization in two dimensional Quantum Gravity
• One-loop quantum gravitational corrections to the scalar two-point function at fixed geodesic distance
• The metric on field space, functional renormalization, and metric-torsion quantum gravity
• An asymptotically safe guide to quantum gravity and matter

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