## Abstract

We show that string theory in AdS_{3} has two distinct phases depending on the radius of curvature R_{AdS} = √kl_{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.

Original language | American English |
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Pages (from-to) | 3-34 |

Number of pages | 32 |

Journal | Nuclear Physics B |

Volume | 719 |

Issue number | 1-2 |

DOIs | |

State | Published - 18 Jul 2005 |

### Bibliographical note

Funding Information:This work has been supported by the EEC contract No. SC1-CT91-0714 (TSTS).

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