Phases of quantum gravity in AdS3 and linear dilaton backgrounds

A. Giveon*, D. Kutasov, E. Rabinovici, A. Sever

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

92 Scopus citations


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, ceff < 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 = √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.

Original languageEnglish
Pages (from-to)3-34
Number of pages32
JournalNuclear Physics B
Issue number1-2
StatePublished - 18 Jul 2005
Externally publishedYes


FundersFunder number
Department of Physics
U.S. Department of Energy
Horowitz Foundation for Social Policy
European CommissionMRTN-CT-2004-512194
Israel Science Foundation
European Forest Institute


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