String theory on AdS(3)

It was shown by Brown and Henneaux that the classical theory of gravity on AdS(3) has an infinite-dimensional symmetry group forming a Virasoro algebr a. More recently, Giveon, Kutasov and Seiberg (GKS) constructed the corresp onding Virasoro generators in the first-quantized string theory on AdS(3). In this paper, we explore various aspects of string theory on AdS(3) and st udy the relation between these two works. We show how semi-classical proper ties of the string theory reproduce many features of the AdS/CFT duality. F urthermore, we examine how the Virasoro symmetry of Brown and Henneaux is r ealized in string theory, and show how it leads to the Virasoro Ward identi ties of the boundary CFT. The Virasoro generators of GKS emerge naturally i n this analysis. Our work clarifies several aspects of the GKS construction : why the Brown-Henneaux Virasoro algebra can be realized on the first-quan tized Hilbert space, to what extent the free-field approximation is valid, and why the Virasoro generators act on the string worldsheet localized near the boundary of AdS(3). On the other hand, we find that the way the centra l charge of the Virasoro algebra is generated is different from the mechani sm proposed by GKS.