Bulk versus boundary dynamics in anti-de Sitter spacetime - art. no. 046003

We investigate the details of the bulk-boundary correspondence in Lorentzia n signature anti-de Sitter space. Operators in the boundary theory couple t o sources identified with the boundary values of non-normalizable bulk mode s. Such modes do not fluctuate and provide classical backgrounds on which b ulk excitations propagate. Normalizable modes in the bulk arise as a set of saddlepoints of the action for a fixed boundary condition. They fluctuate and describe the Hilbert space of physical states. We provide an explicit, complete set of both types of modes for free scalar fields in global and Po incare coordinates. For AdS(3), the normalizable and non-normalizable modes originate in the possible representations of the isometry group SL(2,R)(L) X SL(2,R)(R) for a field of given mass. We discuss the group properties of mode solutions in both global and Poincare coordinates and their relation to different expansions of operators on the cylinder and on the plane. Fina lly, we discuss the extent to which the boundary theory is a useful descrip tion of the bulk spacetime. [S0556-2821(99)07502-5].