de Sitter space and Holography

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