2018/01/31 by Daniel Kabat, Gilad Lifschytz
Mathematics · Physics and Astronomy · #Boundary value problem #Field (mathematics) #Operator (biology) #Operator product expansion #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Quantum #Quantum chaos and dynamical systems #Quantum field theory #Quantum many-body systems #Semiclassical physics #Spectral Theory in Mathematical Physics #hep-th
paper · pdf · doi:10.1007/jhep03(2018)151
22 pages. v2: references added
arxiv created 2018/01/31 · openalex created_date 2018/02/02 · openalex publication_date 2018/03/01 · arxiv updated 2018/04/18 · openalex updated_date 2026/08/05
A bstract 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.