Four-dimensional quantum gravity in the conformal sector

We study the trace-anomaly-induced dynamics of the conformal factor of four-dimensional (4D) quantum gravity. The resulting effective scalar theory is ultraviolet renormalizable, and possesses a nontrivial, infrared stable fixed point. The exact anomalous scaling dimension of the conformal factor at the critical point is derived. We argue that this theory describes 4D gravity at large distances and provides a framework for a dynamical solution of the cosmological-constant problem.