Composite Operators in Asymptotic Safety

Abstract

We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the Asymptotic Safety program.

38 pages

References in corpus (34)

• Exact evolution equation for the effective potential
• Nonperturbative Evolution Equation for Quantum Gravity
• Aspects of the Functional Renormalisation Group
• Optimised Renormalisation Group Flows
• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Fractal Spacetime Structure in Asymptotically Safe Gravity
• Observables in effective gravity
• Local Quantum Gravity
• The Gravitational Two-Loop Counterterm is Asymptotically Safe
• Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety
• Global Flows in Quantum Gravity
• En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
• Background Independence and Asymptotic Safety in Conformally Reduced 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
• Consistent closure of renormalization group flow equations in quantum gravity
• 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
• Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
• Background independence in a background dependent renormalization group
• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
• Conformally reduced quantum gravity revisited
• Background independent exact renormalization group for conformally reduced gravity
• Ultraviolet Fixed Points in Conformal Gravity and General Quadratic Theories
• Fixed point structure of the conformal factor field in quantum gravity
• Quantum Liouville Field Theory as Solution of a Flow Equation
• The unitary conformal field theory behind 2D Asymptotic Safety
• A note on scaling arguments in the effective average action formalism
• Scaling and Renormalization in two dimensional Quantum Gravity
• Bare vs. Effective Fixed Point Action in Asymptotic Safety: The Reconstruction Problem
• Geometrical Properties of Conformal Field Theories Coupled to Two-Dimensional Quantum Gravity

Cited by in corpus (29)

• The nonperturbative functional renormalization group and its applications
• Towards apparent convergence in asymptotically safe quantum gravity
• One force to rule them all: asymptotic safety of gravity with matter
• Asymptotic safety of quantum gravity beyond Ricci scalars
• Dimension and Dimensional Reduction in Quantum Gravity
• Aspects of asymptotic safety for quantum gravity
• Viability of quantum-gravity induced ultraviolet completions for matter
• Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
• Physical renormalization schemes and asymptotic safety in quantum gravity
• Scalar-Tensor theories within Asymptotic Safety
• Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
• Relational observables in Asymptotically safe gravity
• Functional Renormalisation for $f(R_{\mu \nu \rho \sigma })$ Quantum Gravity
• Background Independent Quantum Field Theory and Gravitating Vacuum Fluctuations
• Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
• Fractal geometry of higher derivative gravity
• Geometric operators in the asymptotic safety scenario for quantum gravity
• Operator product expansion coefficients in the exact renormalization group formalism
• On the scaling of composite operators in Asymptotic Safety
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• On characterizing the Quantum Geometry underlying Asymptotic Safety
• Renormalization group flows and fixed points for a scalar field in curved space with nonminimal $F(\varphi )R$ coupling
• Heat kernel coefficients for massive gravity
• A Lorentzian renormalisation group equation for gauge theories
• The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory
• On the possibility of a novel (A)dS/CFT relationship emerging in Asymptotic Safety
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Operator product expansion coefficients from the nonperturbative functional renormalization group
• Composite operators in functional renormalization group approach