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Bulk locality from modular flow
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DOI：10.1007/JHEP07(2017)151.png)
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Abstract
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We study the reconstruction of bulk operators in the entanglement wedge in terms of low energy operators localized in the respective boundary region. To leading order in N, the dual boundary operators are constructed from the modularow of single trace operators in the boundary subregion. The appearance of modular evolved boundary operators can be understood due to the equality between bulk and boundary modularows and explicit formulas for bulk operators can be found with a complete understanding of the action of bulk modularow, a difficult but in principle solvable task. We also obtain an expression when the bulk operator is located on the Ryu-Takayanagi surface which only depends on the bulk to boundary correlator and does not require the explicit use of bulk modularow. This expression generalizes the geodesic operator/OPE block dictionary to general states and boundary regions.
Keywords:
AdS-CFT Correspondence
Conformal Field Theory
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