String theory on AdS3

It was shown by Brown and Henneaux that the classical theory of gravity onAdS_3 has an infinite-dimensional symmetry group forming a Virasoro algebra.More recently, Giveon, Kutasov and Seiberg (GKS) constructed the correspondingVirasoro generators in the first-quantized string theory on AdS_3. In thispaper, we explore various aspects of string theory on AdS_3 and study therelation between these two works. We show how semi-classical properties of thestring theory reproduce many features of the AdS/CFT duality. Furthermore, weexamine how the Virasoro symmetry of Brown and Henneaux is realized in stringtheory, and show how it leads to the Virasoro Ward identities of the boundaryCFT. The Virasoro generators of GKS emerge naturally in this analysis. Our workclarifies several aspects of the GKS construction: why the Brown-HenneauxVirasoro algebra can be realized on the first-quantized Hilbert space, to whatextent the free-field approximation is valid, and why the Virasoro generatorsact on the string worldsheet localized near the boundary of AdS_3. On the otherhand, we find that the way the central charge of the Virasoro algebra isgenerated is different from the mechanism proposed by GKS.Comment: 22 pages, 4 figures, LateX; references added, minor correction