En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions

Abstract

The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a `bi-metric' ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein-Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring. We conclude that the next generation of truncations must be bi-metric.

27 figures. [v2]: Typos in some formulae in appendix A.2 corrected (special thanks to Tugba Buyukbese)

References in corpus (11)

• Exact evolution equation for the effective potential
• Asymptotically Safe Lorentzian Gravity
• Renormalization group improved gravitational actions: a Brans-Dicke approach
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Matter Induced Bimetric Actions for Gravity
• Background Independence and Asymptotic Safety in Conformally Reduced Gravity
• 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
• Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter

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