The Holographic Map as a Conditional Expectation

Abstract: I will demonstrate that holographic error correcting codes naturally give rise to conditional expectations acting on the local operator algebras in the boundary theory. I will use this to give simple derivations of some previously known results as well as some new results when multiple boundary/bulk algebras are considered. Connections to the theory of QFT superselection sectors will be discussed. I will also discuss some shortcomings of these codes as models of AdS/CFT.