Physical renormalization schemes and asymptotic safety in quantum gravity

Abstract

The methods of the renormalization group and the $\epsilon$-expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the $\epsilon$-expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultra-violet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.

43 pages. Version 2: Some clarifying comments added. Conforms with published version

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• Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
• Effective universality in quantum gravity
• Asymptotic safety and field parametrization dependence in the f(R) truncation
• Asymptotic solutions in asymptotic safety
• Essential Quantum Einstein Gravity
• Essential renormalisation group
• Frame (In)equivalence in Quantum Field Theory and Cosmology
• Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
• A curvature bound from gravitational catalysis
• The weak-gravity bound in asymptotically safe gravity-gauge systems
• Is scale-invariance in gauge-Yukawa systems compatible with the graviton?
• Functional Renormalisation for $f(R_{\mu \nu \rho \sigma })$ Quantum Gravity
• Gravity in $d=2+\epsilon$ dimensions and realizations of the diffeomorphisms group
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• Background independent exact renormalisation
• On the scaling of composite operators in Asymptotic Safety
• The search for the universality class of metric quantum gravity
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• On the resilience of the gravitational variational principle under renormalization
• Coarse-graining of the Einstein-Hilbert Action rewritten by the Fisher information metric