Does boundary quantum mechanics imply quantum mechanics in the bulk?
Does boundary quantum mechanics imply quantum mechanics in the bulk?
复制标题
边界量子力学是否意味着整体量子力学？
DOI：
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发表时间：
2018
影响因子：
5.4
通讯作者：
G. Lifschytz
中科院分区：
文献类型：
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作者：
D. Kabat;G. Lifschytz
AdS/CFT中的微扰体重构首先将自由体场ψ（0）表示为CFT中的涂抹算子。一系列的1/N修正必须加到ψ（0）上，以表示相互作用的体场ψ。这些修正已经在文献中从几个角度确定。在这里，我们开发了一个新的视角。我们表明，相关函数涉及到的？（0）遭受由于解析延拓的模糊性。因此，在CFT中，ε（0）不是一个定义良好的线性算子。这意味着体重构可以被理解为在CFT中建立定义良好的算子的过程，从而挑选出相互作用的场。我们进一步提出，将π（0）定义为线性算子的困难可以重新解释为结合性的崩溃。假设在微扰论中，只有将π（0）修正为结合算子。这表明体量子力学仅在半经典体几何的微扰理论中有效。
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.