Phases of quantum gravity in AdS3 and linear dilaton backgrounds

We show that string theory in AdS3 has two distinct phases depending on the radius of curvature RAdS=kls. For k>1 (i.e., RAdS>ls), the SL(2,C) invariant vacuum of the spacetime conformal field theory is normalizable, the high energy density of states is given by the Cardy formula with ceff=c, and generic high energy states look like large BTZ black holes. For k<1, the SL(2,C) invariant vacuum as well as BTZ black holes are non-normalizable, ceff12). The states responsible for this growth are two-dimensional black holes for k>1, and highly excited perturbative strings living in the linear dilaton throat for k<1. The change of behavior at k=1 in the two cases is an example of a string/black hole transition. The entropies of black holes and strings coincide at k=1.