Does boundary quantum mechanics imply quantum mechanics in the bulk?
arXiv:1801.08101 · doi:10.1007/JHEP03(2018)151
Abstract
Perturbative bulk reconstruction in AdS/CFT starts by representing a free bulk field $Ï^{(0)}$ as a smeared operator in the CFT. A series of $1/N$ corrections must be added to $Ï^{(0)}$ to represent an interacting bulk field $Ï$. 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 $Ï^{(0)}$ suffer from ambiguities due to analytic continuation. As a result $Ï^{(0)}$ 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 $Ï$. We further propose that the difficulty with defining $Ï^{(0)}$ as a linear operator can be re-interpreted as a breakdown of associativity. Presumably $Ï^{(0)}$ 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.
22 pages. v2: references added