De sitter invariant vacuum states, vertex operators, and conformal field theory correlators

We show that there is only one physically acceptable vacuum state for quantum fields in de Sitter space-time which is left invariant under the action of the de Sitter-Lorentz group SO(1; d) and supply its physical interpretation in terms of the Poincaré invariant quantum field theory (QFT) on one dimension higher Minkowski space-time. We compute correlation functions of the generalized vertex operator : e^iŜ(x) :, where Ŝ(x) is a massless scalar field, on the d-dimensional de Sitter space and demonstrate that their limiting values at time-like infinities on de Sitter space reproduce correlation functions in (d - 1)-dimensional Euclidean conformal field theory (CFT) on S^d-1 for scalar operators with arbitrary real conformal dimensions. We also compute correlation functions for a vertex operator e ^iŜ(u) on the Lobaczewski space and find that they also reproduce correlation functions of the same CFT. The massless field Ŝ(u) is the nonlocal transform of the massless field Ŝ(x) on de Sitter space introduced by one of us.