  We provide a bottom-up argument to derive some known results from holographic
renormalization using the classical bulk-bulk equivalence of General Relativity
and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The
purpose of this paper is twofold: 1) to advertise the simple classical
mechanism: trading of gauge symmetries, that underlies the bulk-bulk
equivalence of General Relativity and Shape Dynamics to readers interested in
dualities of the type of AdS/CFT; and 2) to highlight that this mechanism can
be used to explain certain results of holographic renormalization, providing an
alternative to the AdS/CFT conjecture for these cases. To make contact with
usual the semiclassical AdS/CFT correspondence, we provide, in addition, a
heuristic argument that makes it plausible why the classical equivalence
between General Relativity and Shape Dynamics turns into a duality between
radial evolution in gravity and the renormalization group flow of a conformal
field theory. We believe that Shape Dynamics provides a new perspective on
gravity by giving conformal structure a primary role within the theory. It is
hoped that this work provides the first steps towards understanding what this
new perspective may be able to teach us about holographic dualities.
