Note on classical string dynamics on AdS3 -: art. no. 126004

We consider bosonic strings propagating on Euclidean anti-de Sitter space (AdS(3)), and study in particular the realization of various worldsheet symmetries. We give a proper definition for the Brown-Henneaux asymptotic target space symmetry, when acting on the string action, and derive the Giveon-Kutasov-Seiberg worldsheet contour integral representation simply by using Noether's theorem. We show that making identifications in the target space is equivalent to the insertion of an (exponentiated) graviton vertex operator carrying the corresponding charge. Finally, we point out an interesting relation between 3D gravity and the dynamics of the worldsheet on AdS3. Both theories are described by an SL(2,C)/SU(2) Wess-Zumino-Witten (WZW) model, and we prove that the reduction conditions determined on one hand by worldsheet diffeomorphism invariance, and on the other by the Brown-Henneaux boundary conditions, are the same. [S0556-2821(99)02124-4].