1211.3494 (Aron C. Wall)

Maximin Surfaces, and the Strong Subadditivity of the Covariant
Holographic Entanglement Entropy    [PDF]

Aron C. Wall

The covariant holographic entropy conjecture of AdS/CFT relates the entropy of a boundary region R to the area of an extremal surface in the bulk spacetime. Assuming that the bulk spacetime is a classical, horizonless, globally hyperbolic manifold obeying the null energy condition, it is proven that these extremal area surfaces i) exist by a maximin construction, ii) always lie outside the causal wedge of R, iii) have less area than the bifurcation surface of the causal wedge, iv) move away from the boundary as R grows, and v) obey strong subadditivity and monogamy of mutual information. These results suggest that the information in R allows the bulk to be reconstructed all the way up to the extremal area surface.

View original: http://arxiv.org/abs/1211.3494