TY - JOUR
T1 - Null geodesics, local CFT operators, and AdS/CFT for subregions
AU - Bousso, Raphael
AU - Freivogel, Ben
AU - Leichenauer, Stefan
AU - Rosenhaus, Vladimir
AU - Zukowski, Claire
PY - 2013/9/27
Y1 - 2013/9/27
N2 - We investigate the nature of the AdS/CFT duality between a subregion of the bulk and its boundary. In global AdS/CFT in the classical GN=0 limit, the duality reduces to a boundary value problem that can be solved by restricting to one-point functions of local operators in the conformal field theory (CFT). We show that the solution of this boundary value problem depends continuously on the CFT data. In contrast, the anti-de Sitter (AdS)-Rindler subregion cannot be continuously reconstructed from local CFT data restricted to the associated boundary region. Motivated by related results in the mathematics literature, we posit that a continuous bulk reconstruction is only possible when every null geodesic in a given bulk subregion has an endpoint on the associated boundary subregion. This suggests that a subregion duality for AdS-Rindler, if it exists, must involve nonlocal CFT operators in an essential way.
AB - We investigate the nature of the AdS/CFT duality between a subregion of the bulk and its boundary. In global AdS/CFT in the classical GN=0 limit, the duality reduces to a boundary value problem that can be solved by restricting to one-point functions of local operators in the conformal field theory (CFT). We show that the solution of this boundary value problem depends continuously on the CFT data. In contrast, the anti-de Sitter (AdS)-Rindler subregion cannot be continuously reconstructed from local CFT data restricted to the associated boundary region. Motivated by related results in the mathematics literature, we posit that a continuous bulk reconstruction is only possible when every null geodesic in a given bulk subregion has an endpoint on the associated boundary subregion. This suggests that a subregion duality for AdS-Rindler, if it exists, must involve nonlocal CFT operators in an essential way.
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U2 - 10.1103/PhysRevD.88.064057
DO - 10.1103/PhysRevD.88.064057
M3 - Article
AN - SCOPUS:84885026386
SN - 1550-7998
VL - 88
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 6
M1 - 064057
ER -