RG flow of Weyl-invariant dilaton gravity

Abstract

Any theory can be made Weyl invariant by introducing a dilaton. It is shown how to construct renormalization group equations for gravity that maintain this property. Explicit calculations are given only in the simplest approximation, namely for the one loop beta functions of a dilaton conformally coupled to a dynamical metric, but the results have wider validity. This formalism could be used to define the meaning of a theory with a position-dependent cutoff: it is equivalent to a theory with a constant cutoff, but a conformally related metric.

To appear in New Journal of Physics. 20 pages

References in corpus (29)

• Conformal Symmetry and the Standard Model
• Asymptotic safety in higher-derivative gravity
• Fixed Points of Higher Derivative Gravity
• Ultraviolet properties of f(R)-Gravity
• Quantum scale invariance, cosmological constant and hierarchy problem
• On the renormalization group flow of f(R)-gravity
• Scale invariance, unimodular gravity and dark energy
• Taming perturbative divergences in asymptotically safe gravity
• Renormalization group improved gravitational actions: a Brans-Dicke approach
• Dark energy: a quantum fossil from the inflationary Universe?
• A class of elementary particle models without any adjustable real parameters
• The Higgs Phenomenon in Quantum Gravity
• Effective Action, Conformal Anomaly and the Issue of Quadratic Divergences
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Background Independence and Asymptotic Safety in Conformally Reduced Gravity
• Scale-invariant alternatives to general relativity
• Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance
• Cosmologies with a time dependent vacuum
• Inflationary solutions in asymptotically safe f(R) theories
• Fixed Points of Nonlinear Sigma Models in d>2
• Renormalization Group Flow of the Holst Action
• Perturbative quantum gravity with the Immirzi parameter
• The Conformal Constraint in Canonical Quantum Gravity
• Probing the small distance structure of canonical quantum gravity using the conformal group
• Relaxing a large cosmological constant
• Asymptotic safety and the gauged SU(N) nonlinear sigma-model
• Fermions and Goldstone bosons in an asymptotically safe model
• The electroweak S and T parameters from a fixed point condition
• A Different Look at Dark Energy and the Time Variation of Fundamental Constants

Cited by in corpus (34)

• Selected topics in scalar-tensor theories and beyond
• Spacetime completeness of non-singular black holes in conformal gravity
• Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
• The Renormalization Group and Weyl-invariance
• Background independent exact renormalization group for conformally reduced gravity
• Unimodular quantum gravity and the cosmological constant
• The path integral of unimodular gravity
• Gravity with more or less gauging
• Fixed point structure of the conformal factor field in quantum gravity
• A link that matters: Towards phenomenological tests of unimodular asymptotic safety
• Frame (In)equivalence in Quantum Field Theory and Cosmology
• Weyl-Invariant Higher Curvature Gravity Theories in n Dimensions
• Split Weyl transformations in quantum gravity
• Brans-Dicke theory in the local potential approximation
• Fake Conformal Symmetry in Unimodular Gravity
• Quantization and fixed points of non-integrable Weyl theory
• Classical Weyl Transverse Gravity
• Trace anomaly and infrared cutoffs
• Non-minimal Tinges of Unimodular Gravity
• The metric on field space, functional renormalization, and metric-torsion quantum gravity
• Planck and Electroweak Scales Emerging from Conformal Gravity
• Curing black hole singularities with local scale invariance
• The Dilaton Wess-Zumino Action in 6 Dimensions from Weyl Gauging: Local Anomalies and Trace Relations
• A modified variational principle for gravity in modified Weyl geometry
• Early universe in quantum gravity
• A Noncompact Weyl-Einstein-Yang-Mills Model: A Semiclassical Quantum Gravity
• Reissner-Nordstrom Solution from Weyl Transverse Gravity
• Modified gravity from Weyl connection and the $f(R,\mathcal{A})$ extension
• Restricted Weyl Symmetry and Spontaneous Symmetry Breakdown of Conformal Symmetry
• On the vector conformal models in an arbitrary dimension
• Weyl-invariant Higher Curvature Gravity Theories in n Dimensions and Mass Generation by Symmetry Breaking
• Non-perturbative quantum Galileon in the exact renormalization group
• Cosmological Weyl-Einsteinian-Cubic Gravity as a Gauge Theory of Gravity
• Local Scale Invariant Kaluza-Klein Reduction