Null geodesics, local CFT operators, and AdS/CFT for subregions

作者：Bousso Raphael^*; Freivogel Ben; Leichenauer Stefan; Rosenhaus Vladimir; Zukowski Claire

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2013, 88(6): 064057.

DOI：10.1103/PhysRevD.88.064057

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 G(N) = 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.

• 出版日期2013-9-27