De Sitter Invariant Vacuum States, Vertex Operators, and Conformal Field Theory Correlators

Details De Sitter Invariant Vacuum States, Vertex Operators, and Conformal Field Theory Correlators De Sitter Invariant Vacuum States, Vertex Operators, and Conformal Field Theory Correlators

2003-01-06

arxiv.org/abs/hep-th/0301023v2

Acta Phys.Polon.B42:1207-1218,2011

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, LaTeX file We thank Roman Jackiw for bringing to our attention Ref. 16

Scientific paper

10.5506/APhysPolB.42.1207

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 Poincare invariant quantum field theory (QFT) on one dimension higher Minkowski spacetime. We compute correlation functions of the generalized vertex operator $:e^{i\hat{S}(x)}:$, where $\hat{S}(x)$ is a massless scalar field, on the $d$-dimensional de Sitter space and demonstrate that their limiting values at timelike 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 $e^{i\hat{S}(u)}$ on the \L obaczewski space and find that they also reproduce correlation functions of the same CFT. The massless field $\hat{S}(u)$ is the nonlocal transform of the massless field $\hat{S}(x)$ on de Sitter space introduced by one of us.

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