de Sitter space and Holography

The metric is given bydS 2 = −dτ 2 + l 2 cosh 2 τl dΩ2 d−1In this coordinates dS d space looks like a d − 1 sphere whichstarts out infinity large at τ = −∞ then shrinks to its minimumfinite size that τ = 0 and then grows again to infinite size atτ = ∞.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-defined10