Fixed point structure of the conformal factor field in quantum gravity

Abstract

The $\mathcal{O}({\partial }^2)$ background independent flow equations for conformally reduced gravity are shown to be equivalent to flow equations naturally adapted to scalar field theory with a wrong sign kinetic term. This sign change is shown to have a profound effect on the renormalization group properties, broadly resulting in a continuum of fixed points supporting both a discrete and a continuous eigenoperator spectrum, the latter always including relevant directions. The properties at the Gaussian fixed point are understood in particular depth, but also detailed studies of the local potential approximation, and the full $\mathcal{O}({\partial }^2)$ approximation are given. These results are related to evidence for asymptotic safety found by other authors.

58 pages, 15 figures. Added section that shows that for any sensible cutoff profile, space-time and field dimension, the LPA for standard scalar field theory can only have a discrete set of fixed points, while the sign change of the kinetic term results instead in a continuum of fixed points

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• Asymptotically Safe $f(R)$-Gravity Coupled to Matter II: Global Solutions
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