  Using holographic renormalization coupled with the
Caffarelli/Silvestre\cite{caffarelli} extension theorem, we calculate the
precise form of the boundary operator dual to a bulk scalar field rather than
just its average value. We show that even in the presence of interactions in
the bulk, the boundary operator dual to a bulk scalar field is an anti-local
operator, namely the fractional Laplacian. The propagator associated with such
operators is of the general power-law (fixed by the dimension of the scalar
field) type indicative of the absence of particle-like excitations at the
Wilson-Fisher fixed point or the phenomenological unparticle construction.
Holographic renormalization also allows us to show how radial quantization can
be extended to such non-local conformal operators.
