Hagedorn strings in AdS3

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 I-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 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.