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arXiv · 1801.08101

Does boundary quantum mechanics imply quantum mechanics in the bulk?

Daniel Kabat·Gilad Lifschytz
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Abstract

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.

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Daniel Kabat, Gilad Lifschytz. 2018-01-31. Does boundary quantum mechanics imply quantum mechanics in the bulk?. https://doi.org/10.1007/jhep03(2018)151

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