Does boundary quantum mechanics imply quantum mechanics in the bulk?
- 75 Downloads
Perturbative bulk reconstruction in AdS/CFT starts by representing a free bulk field ϕ(0) as a smeared operator in the CFT. A series of 1/N corrections must be added to ϕ(0) to represent an interacting bulk field ϕ. 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 ϕ(0) suffer from ambiguities due to analytic continuation. As a result ϕ(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 ϕ. We further propose that the difficulty with defining ϕ(0) as a linear operator can be re-interpreted as a breakdown of associativity. Presumably ϕ(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.
KeywordsAdS-CFT Correspondence Models of Quantum Gravity
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.