Lecture 12: Holography of information in AdS
In this lecture, we first discussed some additional aspects of the Reeh-Schlieder theorem from Lecture 11. A Mathematica file with some simple numerical examples that demonstrate our result can be downloaded here.
Download Mathematica demonstration of how to generate states from a small time band
In this lecture, we proved the principle of holography of information for theories of gravity in asymptotically AdS spacetimes. Gravity is different from other quantum field theories because the projector on the vacuum belongs to the algebra of asymptotic operators; in no other theory can one use an operator from the asymptotic algebra to project onto a unique state. When this observation is combined with the Reeh-Schlieder theorem that we proved in Lecture 11, we find a remarkable result: in a theory of gravity in an asymptotically AdS spacetime, any two distinct states in the Hilbert space can be distinguished by operators from an infinitesimal band on the boundary.
This result is obvious when viewed from the perspective of AdS/CFT but we did not invoke AdS/CFT in deriving it. So this result can be viewed as an ab initio explanation of an important aspect of AdS/CFT and
also for the fact that only gravitational theories are holographic.
