Shape Dynamics and AdS/CFT

I present a semi-classical correspondence between three-dimensional euclidean conformal field theory and the large-volume dynamics of gravity with positive cosmological constant in 3+1 dimensions. The correspondence is based on a theory of gravity called Shape Dynamics, whose solutions are a subset of those of General Relativity, namely those that can be foliated with constant mean extrinsic curvature. Shape Dynamics makes it possible to solve exactly for all the local degrees of freedom, while in GR this is possible only approximately, within a derivative expansion, due to the non-linearity of the scalar constraint.