TY - JOUR
T1 - Bulk locality from modular flow
AU - Faulkner, Thomas
AU - Lewkowycz, Aitor
N1 - Publisher Copyright:
© 2017, The Author(s).
PY - 2017/7/1
Y1 - 2017/7/1
N2 - 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 modular flow 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 modular flows and explicit formulas for bulk operators can be found with a complete understanding of the action of bulk modular flow, 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 modular flow. This expression generalizes the geodesic operator/OPE block dictionary to general states and boundary regions.
AB - 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 modular flow 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 modular flows and explicit formulas for bulk operators can be found with a complete understanding of the action of bulk modular flow, 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 modular flow. This expression generalizes the geodesic operator/OPE block dictionary to general states and boundary regions.
KW - AdS-CFT Correspondence
KW - Conformal Field Theory
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U2 - 10.1007/JHEP07(2017)151
DO - 10.1007/JHEP07(2017)151
M3 - Article
AN - SCOPUS:85026821693
SN - 1126-6708
VL - 2017
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 7
M1 - 151
ER -