### Abstract

Motivated by the possibility of formulating a strings/black hole correspondence in AdS space, we extract the Hagedorn behavior of thermal AdS_{3} bosonic string from 1-loop partition function of SL(2,R) WZW model. We find that the Hagedorn temperature is monotonically increasing as the AdS radius shrinks, reaches a maximum of order of string scale set by the unitarity bound of the CFT for internal space. The resulting density of states near the Hagedorn temperature resembles the form as for strings in flat space and is dominated by the space-like long string configurations. We then argue a conjectured strings/black hole correspondence in AdS space by applying the Hagedorn thermodynamics. We find the size of the corresponding black hole is a function of the AdS radius. For large AdS radius a black hole far bigger than the string scale will form. On the contrary, when the AdS and string scales are comparable a string size black hole will form. We also examine strings on BTZ background obtained through SL(2,Z) transformation. We find a tachyonic divergence for a BTZ black hole of string scale size.

Original language | English |
---|---|

Article number | 042 |

Journal | Journal of High Energy Physics |

Volume | 2007 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2007 Sep 1 |

### Fingerprint

### Keywords

- Black holes in string theory
- Bosonic strings

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

_{3}.

*Journal of High Energy Physics*,

*2007*(9), [042]. https://doi.org/10.1088/1126-6708/2007/09/042

**Hagedorn strings and correspondence principle in AdS _{3}.** / Lin, Feng Li; Matsuo, Toshihiro; Tomino, Dan.

Research output: Contribution to journal › Article

_{3}',

*Journal of High Energy Physics*, vol. 2007, no. 9, 042. https://doi.org/10.1088/1126-6708/2007/09/042

_{3}. Journal of High Energy Physics. 2007 Sep 1;2007(9). 042. https://doi.org/10.1088/1126-6708/2007/09/042

}

TY - JOUR

T1 - Hagedorn strings and correspondence principle in AdS3

AU - Lin, Feng Li

AU - Matsuo, Toshihiro

AU - Tomino, Dan

PY - 2007/9/1

Y1 - 2007/9/1

N2 - Motivated by the possibility of formulating a strings/black hole correspondence in AdS space, we extract the Hagedorn behavior of thermal AdS3 bosonic string from 1-loop partition function of SL(2,R) WZW model. We find that the Hagedorn temperature is monotonically increasing as the AdS radius shrinks, reaches a maximum of order of string scale set by the unitarity bound of the CFT for internal space. The resulting density of states near the Hagedorn temperature resembles the form as for strings in flat space and is dominated by the space-like long string configurations. We then argue a conjectured strings/black hole correspondence in AdS space by applying the Hagedorn thermodynamics. We find the size of the corresponding black hole is a function of the AdS radius. For large AdS radius a black hole far bigger than the string scale will form. On the contrary, when the AdS and string scales are comparable a string size black hole will form. We also examine strings on BTZ background obtained through SL(2,Z) transformation. We find a tachyonic divergence for a BTZ black hole of string scale size.

AB - Motivated by the possibility of formulating a strings/black hole correspondence in AdS space, we extract the Hagedorn behavior of thermal AdS3 bosonic string from 1-loop partition function of SL(2,R) WZW model. We find that the Hagedorn temperature is monotonically increasing as the AdS radius shrinks, reaches a maximum of order of string scale set by the unitarity bound of the CFT for internal space. The resulting density of states near the Hagedorn temperature resembles the form as for strings in flat space and is dominated by the space-like long string configurations. We then argue a conjectured strings/black hole correspondence in AdS space by applying the Hagedorn thermodynamics. We find the size of the corresponding black hole is a function of the AdS radius. For large AdS radius a black hole far bigger than the string scale will form. On the contrary, when the AdS and string scales are comparable a string size black hole will form. We also examine strings on BTZ background obtained through SL(2,Z) transformation. We find a tachyonic divergence for a BTZ black hole of string scale size.

KW - Black holes in string theory

KW - Bosonic strings

UR - http://www.scopus.com/inward/record.url?scp=34948838287&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34948838287&partnerID=8YFLogxK

U2 - 10.1088/1126-6708/2007/09/042

DO - 10.1088/1126-6708/2007/09/042

M3 - Article

AN - SCOPUS:34948838287

VL - 2007

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 9

M1 - 042

ER -