Phases of quantum gravity in [formula omitted] and linear dilaton backgrounds

Abstract

We show that string theory in AdS 3 has two distinct phases depending on the radius of curvature R AdS = 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 AdS 3 and become more and more weakly coupled there. A similar picture is found in asymptotically linear dilaton spacetime with dilaton gradient Q = 2 / k . The entropy grows linearly with the energy in this case (for k > 1 2 ). 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 .