On the ultraviolet behavior of conformally reduced quadratic gravity

Abstract

We study the conformally reduced $R+R^2$ theory of gravity and we show that the theory is asymptotically safe with an ultraviolet critical manifold of dimension three. In particular, we discuss the universality properties of the fixed point and its stability under the use of different regulators with the help of the proper-time flow equation. We find three relevant directions, corresponding to the $\sqrt{g}$, $\sqrt{g}R$ and $\sqrt{g}{R}^2$ operators, whose critical properties are very similar to the ones shared by the full theory. Our result shows that the basic mechanism at the core of the Asymptotic Safety program is still well described by the conformal sector also beyond the Einstein-Hilbert truncation. Possible consequences for the asymptotic safety program are discussed.

14 pages, 4 figures

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• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Ising exponents from the functional renormalisation group
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Cited by in corpus (3)

• Regular Black Holes from Proper-Time flow in Quantum Gravity and their Quasinormal modes, Shadow and Hawking radiation
• Thermal RG Flow of AS Quantum Gravity
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory