de Sitter space and Holography

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dS static patch (spatial)dg =0 g =1 g =000 00 00o SCFT on dS d−1CFT on dS d−1Localized graviton1E=0 E= E=0R• D-brane probes of this region exhibit the same physics:Both are equivalent to CFT on dS d−1 for energy 0 < E ≪ 1 R .• Probes constructed from bulk gravitons range from energy0 up to 1/R and upon dimensional reduction their spectrumexhibits the mass gap expected of d − 1 dimensional CFT ondS.• Dimensionally reducing to d − 1 dimensional effective fieldtheory also yields a finite d−1 dimensional Plank mass→ Lowerdimensional theory has also gravity.46
Let us consider pure gravity in d dimensional dS space. Thedifferential equations of linearized gravity can be recast to aone dimensional quantum mechanical system with the followingpotentialV = 1 l((d − 2) 24−d(d − 2)41cosh 2 zl)It is a volcano shape potential which has a single bound stateat zero energy, separated from a continuum modes by a massgap of order 1 l 2 .The zero mode solution is(ψ = cosh 2 zl) (2−d)/2It is a normalizable solution to the wave equation with E = 0.Therefore there is a d −1 dimensional graviton on the centralslice at z = 0.One may also write the lower dimensional Planck scale interms of d dimensional theoryM d−3d−1 = lMd−2 d47
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 44 and 45: lim dtdtr→∞∫I ′ dφdφ ′
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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