Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance

Understand

We explore the nonperturbative renormalization group flow of Quantum Einstein Gravity (QEG) on an infinite dimensional theory space.

• We consider "conformally reduced" gravity where only fluctuations of the conformal factor are quantized and employ the Local Potential Approximation for its effective average action.
• The requirement of "background independence" in quantum gravity entails a partial differential equation governing the scale dependence of the potential for the conformal factor which differs significantly from that of a scalar matter field.
• In the infinite dimensional space of potential functions we find a Gaussian as well as a non-Gaussian fixed point which provides further evidence for the viability of the asymptotic safety scenario.