de Sitter space and Holography

Conformal coordinates: T, θ i , i = 1, · · · ,d − 1Looking at the metric in the global coordinates one may writedS 2= cosh 2 τl (− dτ2cosh 2 + l 2 dΩ 2 τ d−1)l1 (=cos 2 T −dT 2 + l 2 dΩ 2 d−1)lwherecosh τ l = 1cos T l, − π 2 < T l < π 2There is one-to-one correspondence between this and the globalcoordinates and therefore it covers entire space.In this coordinates system•∂∂θ d−1is the only Killing vector•∂∂τis NOT a Killing vector• This breaks conservation of the energy so the Hamiltonianis not well-defined11