CRITICALITY AND SCALING IN 4D QUANTUM-GRAVITY

We present a simple argument which determines the critical value of th e anomaly coefficient in four dimensional conformal factor quantum gra vity, at which a phase transition between a smooth and elongated phase should occur. The argument is based on the contribution of singular c onfigurations (''spikes'') which dominate the partition function in th e infrared, The critical value is the analog of c = 1 in the theory of random surfaces, and the phase transition is similar to the Berezensk ii-Kosterlitz-Thouless transition. The critical value we obtain is in agreement with the previous canonical analysis of physical states of t he conformal factor and may explain why a smooth phase of quantum grav ity has not yet been observed in simplicial simulations. We also reder ive the scaling relations in the smooth phase in light of this determi nation of the critical coupling.