de Sitter space and Holography

Now let us repeat the same exercise for the gravitationalaction with position dependent G N . The position dependenceof M d is M d (z) = tanh(z)M d which gives an extra factor oftanh d−2 (z). Up to terms that remain finite as z → 0S on−shell ==∫∫tanh d−2 dz(z)sinh d (z)1 dzsinh 2 (z) cosh d (z) = −1z + O(z)For all d the only divergent term is a universal − 1 zand thereare no logarithms. The conformal anomaly vanishes.One possible interpretation:• Lower dimensional gravity screens the central charge tobe zero, just like is well known from 2d gravity on stringtheory worldsheets. In this scenario one does not even need aconformal field theory beyond scales 1/R since the gravitationaldressing will also make any FT a CFT.• In the same spirit the universal UV dimension of the scalarfields can be understood as gravitational dressing.55