de Sitter space and Holography

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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
4. dS/dS correspondenceStatement of de Sitter HolographyThe dS d static patch is dual to two conformal field theories ondS d−1 cut off at an energy scale 1/R and coupled to eachother as well as to (d − 1)-dimensional gravity.The static patch of d-dimensional dS space with radius Rcan be foliated by dS d−1 slices(ds 2 = sin 2 w)Rds 2 ds d−1+ dw 2OSThe warp factor sin 2 (w/R) is maximal with the finite valueat central slice w = πR/2 and dropping monotonically on eachside until reaches zero at the horizon w = 0, π.The region near horizon (low energy in static patch) isisomorphic to d-dimensional AdS space foliated by dS d−1 slicesand hence constitutes a CFT on dS d−1 at low energy.45
Page 1 and 2: de Sitter space and HolographyThird
Page 3: 1. Historical review and motivation
Page 7 and 8: 5. Technologies:There are a number
Page 9 and 10: Let us know study different coordin
Page 11 and 12: Conformal coordinates: T, θ i , i
Page 13 and 14: Planer (Inflationary) coordinates:
Page 15 and 16: The corresponding metric isdS 2 =
Page 17 and 18: It is easy to see thatX 0 + X d =
Page 20 and 21: 1.2 Causal structure (Penrose diagr
Page 22 and 23: IINorth PoleOSouth PoleNorth PoleOS
Page 24 and 25: The entire region of the dS space i
Page 26 and 27: For example• In static coordinate
Page 28 and 29: An observer moving along a timelike
Page 30 and 31: 3. dS/CFT correspondenceFrom what w
Page 32 and 33: In d dimensions the Einstein equati
Page 34 and 35: One can generalize it for a general
Page 36 and 37: • One can always decompose the me
Page 38 and 39: Consider the Brown-York stress tens
Page 40 and 41: Using the definition of Brown-York
Page 42 and 43: Using this diffeomorphism one may s
Page 46 and 47: dS static patch (spatial)dg =0 g =1
Page 48 and 49: • Lower dimensional Plank mass is
Page 50 and 51: One can use AdS/CFT correspondence
Page 52 and 53: Under this conformal map one has:
Page 54 and 55: Conformal AnomalyAdS/CFT instructs
Page 56 and 57: • Naively one would think that gr
Page 58: This talk is based on the following

de Sitter space and Holography

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