de Sitter space and Holography

lim dtdtr→∞∫I ′ dφdφ ′ (rr ′ ) 2− l(2)Φ(r, t, φ) ∂ ↔ r∗ G(r, t, φ;r ′ , t ′ , φ ′ ) ∂ ↔ r′ ∗Φ(r ′ , t ′ , φ ′ )where dr ∗ = (−V (r)) −1/2 dr.Using the Green function we find〈O(t, φ)O(t ′ ,φ ′ )〉 =const.(cosh ∆tl− cos∆φ) h +The dimension of the CFT operator is given by h + whichcould be complex for highly massive scalar field. So the CFTcould be non-unitary!We note however that in studying this correspondence oneuses the dS in the planer patch. So it is nature to ask:How does the holography for dS space work for otherpatches?44