  Perturbative bulk reconstruction in AdS/CFT starts by representing a free
bulk field $\phi^{(0)}$ as a smeared operator in the CFT. A series of $1/N$
corrections must be added to $\phi^{(0)}$ to represent an interacting bulk
field $\phi$. These corrections have been determined in the literature from
several points of view. Here we develop a new perspective. We show that
correlation functions involving $\phi^{(0)}$ suffer from ambiguities due to
analytic continuation. As a result $\phi^{(0)}$ fails to be a well-defined
linear operator in the CFT. This means bulk reconstruction can be understood as
a procedure for building up well-defined operators in the CFT which thereby
singles out the interacting field $\phi$. We further propose that the
difficulty with defining $\phi^{(0)}$ as a linear operator can be
re-interpreted as a breakdown of associativity. Presumably $\phi^{(0)}$ can
only be corrected to become an associative operator in perturbation theory.
This suggests that quantum mechanics in the bulk is only valid in perturbation
theory around a semiclassical bulk geometry.

High Energy Physics - Theory