de Sitter space and Holography

More documents

Recommendations

Info

Using the definition of Brown-York stress tensor one findsT zz = 1 [h zz − ∂ z h tz + 1 ]4G2 ∂ th zz + O(h 2 )T z¯z = 1 [ 14G 4 e−2t h tt − h z¯z + 1 ]2 (∂¯zh tz + ∂ z h t¯z − ∂ t h z¯z+O(h 2 )Requiring the stress tensor to be finite one leads to theboundary conditionsg z¯z = e−2t2 + O(1),g tt = −1 + O(1),g zz = O(1),= O(1).g tzThe most general diffeomorphism ξ which preserves thisboundary conditions can be written asξ = U(z)∂ z + 1 2 U ′ (z)∂ t + O(e 2t ) + C.C.From bulk dS 3 theory this is a diffeomorphism while fromboundary point of it is two dimensional diffeomorphism of thecomplex plane and a Weyl transformation.40
A three dimensional diffeomorphism is equivalent to a twodimensional conformal transformation.The asymptotic symmetry group of gravity in dS 3 is theconformal group of the complex planeThis is a first hint that the dual theory is a Euclidean conformalfield theory.41
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 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 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

Create successful ePaper yourself

Delete template?

Save as template?