RG flows of Quantum Einstein Gravity in the linear-geometric approximation

Abstract

We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the structure of the new flow equation is considerably simpler than the standard Quantum Einstein Gravity construction since only transverse-traceless and trace part of the metric fluctuations propagate in loops. The geometric flow reproduces the phase-diagram of the Einstein-Hilbert truncation including the non-Gaussian fixed point essential for Asymptotic Safety. Extending the analysis to the polynomial $f(R)$-approximation establishes that this fixed point comes with similar properties as the one found in metric Quantum Einstein Gravity; in particular it possesses three UV-relevant directions and is stable with respect to deformations of the regulator functions by endomorphisms.

32 pages, 4 figues

References in corpus (20)

• Quantum Gravity at a Lifshitz Point
• Ultraviolet properties of f(R)-Gravity
• On the renormalization group flow of f(R)-gravity
• Asymptotically Safe Lorentzian Gravity
• Taming perturbative divergences in asymptotically safe gravity
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Matter Induced Bimetric Actions for Gravity
• Background Independence and Asymptotic Safety in Conformally Reduced Gravity
• Second- and First-Order Phase Transitions in CDT
• Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity
• Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance
• Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
• Fixed-Functionals of three-dimensional Quantum Einstein Gravity
• The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
• The Conformal Constraint in Canonical Quantum Gravity
• The phase diagram of quantum gravity from diffeomorphism-invariant RG-flows
• Living with Infinities
• Fixed Functionals in Asymptotically Safe Gravity
• Fixed points and infrared completion of quantum gravity
• Renormalization of lattice-regularized quantum gravity models I. General considerations