Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface

Abstract

We study quantum effects in higher curvature extensions of general relativity using the functional renormalisation group. New flow equations are derived for general classes of models involving Ricci scalar, Ricci tensor, and Riemann tensor interactions. Our method is applied to test the asymptotic safety conjecture for quantum gravity with polynomial Riemann tensor interactions of the form $\sim \int \sqrt{g}(R_{\mu \nu \sigma \tau }{R}^{\mu \nu \sigma \tau }{)}^n$ and $\sim \int \sqrt{g}R\cdot (R_{\mu \nu \sigma \tau }{R}^{\mu \nu \sigma \tau }{)}^n$, and functions thereof. Interacting fixed points, universal scaling dimensions, gaps in eigenvalue spectra, quantum equations of motion, and de Sitter solutions are identified by combining high order polynomial approximations, Padé resummations, and full numerical integration. Most notably, we discover that quantum-induced shifts of scaling dimensions can lead to a four-dimensional ultraviolet critical surface. Increasingly higher-dimensional interactions remain irrelevant and show near-Gaussian scaling and signatures of weak coupling. Moreover, a new equal weight condition is put forward to identify stable eigenvectors to all orders in the expansion. Similarities and differences with results from the Einstein-Hilbert approximation, $f(R)$ approximations, and $f(R,{\mathrm{Ric}}^2)$ models are highlighted and the relevance of findings for quantum gravity and the asymptotic safety conjecture is discussed.

62 pages, 28 figures. Added more discussions and explanations. Revised several plots. Version accepted for publication with PRD

References in corpus (36)

• Exact evolution equation for the effective potential
• Asymptotic safety in higher-derivative gravity
• Fixed Points of Higher Derivative Gravity
• Ultraviolet properties of f(R)-Gravity
• On the renormalization group flow of f(R)-gravity
• On Holographic Entanglement Entropy and Higher Curvature Gravity
• Asymptotic safety guaranteed
• Asymptotically Safe Lorentzian Gravity
• Taming perturbative divergences in asymptotically safe gravity
• Fixed points of quantum gravity in extra dimensions
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Asymptotic safety in the f(R) approximation
• 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
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Ising exponents from the functional renormalisation group
• The local potential approximation in quantum gravity
• The Universal RG Machine
• Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity
• Correlation functions on a curved background
• Inflationary solutions in asymptotically safe f(R) theories
• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
• Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
• On fixed points of quantum gravity
• On the UV structure of quantum unimodular gravity
• Asymptotically Safe Cosmology
• Asymptotic solutions in asymptotic safety
• On avoiding Ostrogradski instabilities within Asymptotic Safety
• Asymptotic safety guaranteed in supersymmetry
• Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation
• Composite Operators in Asymptotic Safety
• Critical $O(N)$ models in the complex field plane
• Asymptotic safety with Majorana fermions and new large N equivalences
• Non-Gaussian fixed points in fermionic field theories without auxiliary Bose-fields
• Functional Renormalisation for $f(R_{\mu \nu \rho \sigma })$ Quantum Gravity
• Line of Fixed Points in Gross-Neveu Theories

Cited by in corpus (13)

• Essential Quantum Einstein Gravity
• The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking
• Asymptotic freedom and safety in quantum gravity
• Provable properties of asymptotic safety in $f(R)$ approximation
• Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge
• $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the Asymptotically Safe Standard Model
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Lectures in Quantum Gravity
• Ruling out models of vector dark matter in asymptotically safe quantum gravity
• Towards a Higgs mass determination in asymptotically safe gravity with a dark portal
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• Indications against dynamical CPT symmetry restoration in quantum gravity
• Charting GLOBs in Asymptotically Safe Gravity