Phases of Quantum Gravity in AdS3 and Linear Dilaton Backgrounds
A. Giveon, D. Kutasov, E. Rabinovici, A. Sever
Abstract
We show that string theory in AdS3 has two distinct phases depending on the radius of curvature R_{AdS}=\sqrt{k}l_s. For k>1 (i.e. R_{AdS}>l_s), 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 c_{eff}=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, c_{eff}<c, and high energy states correspond to long strings that extend to the boundary of AdS3 and become more and more weakly coupled there. A similar picture is found in asymptotically linear dilaton spacetime with dilaton gradient Q=\sqrt{2/k}. The entropy grows linearly with the energy in this case (for k>\half). 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.