Does boundary quantum mechanics imply quantum mechanics in the bulk?

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Regular Article - Theoretical Physics
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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.

Keywords

AdS-CFT Correspondence Models of Quantum Gravity 

Notes

Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Physics and Astronomy, Lehman CollegeCity University of New YorkBronxU.S.A.
  2. 2.Department of Mathematics and Haifa Research Center for Theoretical Physics and AstrophysicsUniversity of HaifaHaifaIsrael

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