Towards the determination of the dimension of the critical surface in asymptotically safe gravity

Abstract

We compute the beta functions of Higher Derivative Gravity within the Functional Renormalization Group approach, going beyond previously studied approximations. We find that the presence of a nontrivial Newtonian coupling induces, in addition to the free fixed point of the one-loop approximation, also two nontrivial fixed points, of which one has the right signs to be free from tachyons. Our results are consistent with earlier suggestions that the dimension of the critical surface for pure gravity is three.

arXiv commentV2: Some comments and a ref. are added. The full beta functions have been made available in a Mathematica file at https://doi.org/10.5281/zenodo.4017671 and a detailed derivation of the beta functions is given in the ancillary file on this arXiv page. V3: Minor corrections

References in corpus (34)

• Nonperturbative Evolution Equation for Quantum Gravity
• On Renormalization Group Flows in Four Dimensions
• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Asymptotic safety in higher-derivative gravity
• Fixed Points of Higher Derivative Gravity
• Ultraviolet properties of f(R)-Gravity
• Further evidence for asymptotic safety of quantum gravity
• Taming perturbative divergences in asymptotically safe gravity
• Aspects of Quadratic Gravity
• Quadratic Gravity
• Unitarity, stability and loops of unstable ghosts
• Asymptotic safety of quantum gravity beyond Ricci scalars
• Benign vs malicious ghosts in higher-derivative theories
• Higher Derivative Quantum Gravity with Gauss-Bonnet Term
• Conformal Symmetry and Central Charges in 4 Dimensions
• Agravity up to infinite energy
• Aspects of asymptotic safety for quantum gravity
• Solution to the ghost problem in fourth order derivative theories
• Conformal Quantum Gravity with the Gauss-Bonnet Term
• Covariant methods for the calculation of the effective action in quantum field theory and investigation of higher-derivative quantum gravity
• Quantum Gravity, Fakeons And Microcausality
• Higher Derivative Gravity and Asymptotic Safety in Diverse Dimensions
• Ghost-free higher-derivative theory
• A QCD analogy for quantum gravity
• Gauges and functional measures in quantum gravity II: Higher derivative gravity
• Ultraviolet Fixed Points in Conformal Gravity and General Quadratic Theories
• Higher Derivative Gravity from the Universal Renormalization Group Machine
• Criticality and Scaling in 4D Quantum Gravity
• Quartic propagators, negative norms and the physical spectrum
• Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
• A bootstrap strategy for asymptotic safety
• Off-diagonal heat-kernel expansion and its application to fields with differential constraints
• The c and a-theorems and the Local Renormalisation Group

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• $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the Asymptotically Safe Standard Model
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Asymptotically Safe Hilbert-Palatini Gravity in an On-Shell Reduction Scheme
• Towards a Higgs mass determination in asymptotically safe gravity with a dark portal
• 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
• Indications against dynamical CPT symmetry restoration in quantum gravity
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