Fixed point structure of the conformal factor field in quantum gravity

Understand

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.