Universality and symmetry breaking in conformally reduced quantum gravity

Abstract

The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group trajectories obtained by projecting the flow on a flat topology are more stable than those obtained from a projection on a spherical topology. In the latter case the ultraviolet flow can be characterized by a Hopf bifurcation with an ultraviolet attractive limiting cycle. Although the possibility of determining the infrared flow for an extended theory space can be severely hampered due to the conformal factor instability, we present a robust numerical approach to study the flow structure around the non-gaussian fixed point as an inverse-problem strategy. In particular it is shown the possibility of having a spontaneous breaking of the diffeomorphism invariance can be realized with non-local functionals of the volume operator.

16 pages, 5 figures; replaced with journal version

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• Cosmological bounds on the field content of asymptotically safe gravity-matter models
• Faddeev-Popov ghosts in quantum gravity beyond perturbation theory
• One-loop renormalization in a toy model of Horava-Lifshitz gravity
• Fixed point structure of the conformal factor field in quantum gravity
• Infinite order quantum-gravitational correlations
• Manifestly diffeomorphism invariant classical Exact Renormalization Group
• Modulated Ground State of Gravity Theories with Stabilized Conformal Factor
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• Critical exponents in quantum Einstein gravity
• Renormalization group properties of the conformal mode of a torus
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• RG flows of Quantum Einstein Gravity in the linear-geometric approximation
• Thermal RG Flow of AS Quantum Gravity
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory
• Functional truncations in asymptotic safety for quantum gravity