Phases of quantum gravity in image and linear dilaton backgrounds Original Research Article

We show that string theory in image has two distinct phases depending on the radius of curvature image. For image (i.e., image), the image invariant vacuum of the spacetime conformal field theory is normalizable, the high energy density of states is given by the Cardy formula with image, and generic high energy states look like large BTZ black holes. For image, the image invariant vacuum as well as BTZ black holes are non-normalizable, image, and high energy states correspond to long strings that extend to the boundary of image and become more and more weakly coupled there. A similar picture is found in asymptotically linear dilaton spacetime with dilaton gradient image. The entropy grows linearly with the energy in this case (for image). The states responsible for this growth are two-dimensional black holes for image, and highly excited perturbative strings living in the linear dilaton throat for image. The change of behavior at image in the two cases is an example of a string/black hole transition. The entropies of black holes and strings coincide at image.