de Sitter space and Holography

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• Lower dimensional Plank mass is consistent with thatgenerated by a renormalization of Newton constant from Sdegrees of freedom cut off at the scale 1/R.(11∼ M d−3d−1G ∼ RMd−2 d∼ (RM d ) d−2N,d−1 R( d−3 1∼ SR)) d−3∼SM d−3UVThe pictureWritten in a dS d−1 slicing, dS d has the form of a Randall-Sundrum system.g00
In the RS construction one truncates the warp factor at afinite value of the radial coordinate by including a brane sourcewith extra degree of freedom. In the dS case, the additionalbrane source is unnecessary.A smooth UV brane at which the warp factor turns around isbuilt in to the geometry.BULKBRANEM d−1QuantumGravityMdClassical Gravityin dS d?1/LGravity + 2 CFTsin dS d−1M dL>>1• On d-dimensional gravity side, one has local effective fieldtheory up to M d ≫ 1/R.• Above M d quantum gravity effects become important inthe bulk and one has to UV complete the system.• Using gravity side one can study the d − 1 dimensionaltheory in the range of energy 1/R < E < M d .49
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 46 and 47: dS static patch (spatial)dg =0 g =1
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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