Does boundary quantum mechanics imply quantum mechanics in the bulk?

Abstract

Perturbative bulk reconstruction in AdS/CFT starts by representing a free bulk field ${\varphi }^{(0)}$ as a smeared operator in the CFT. A series of $1/N$ corrections must be added to ${\varphi }^{(0)}$ to represent an interacting bulk field $\varphi$. 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 ${\varphi }^{(0)}$ suffer from ambiguities due to analytic continuation. As a result ${\varphi }^{(0)}$ 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 $\varphi$. We further propose that the difficulty with defining ${\varphi }^{(0)}$ as a linear operator can be re-interpreted as a breakdown of associativity. Presumably ${\varphi }^{(0)}$ 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

References in corpus (4)

• Bulk locality from modular flow
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• An Exact Operator That Knows Its Location
• Local bulk physics from intersecting modular Hamiltonians

Cited by in corpus (9)

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• Interactions resolve state-dependence in a toy-model of AdS black holes
• Bulk reconstruction in rotating BTZ black hole
• Lectures on Bulk Reconstruction
• Dressing bulk fields in AdS${}_3$
• Reconstructing bulk equation of motion using CFT modular Hamiltonians
• Regge OPE blocks and light-ray operators
• Dressing bulk spinor fields in AdS${}_3$
• Bulk reconstruction and Bogoliubov transformations in AdS${}_2$