Causal connectability between quantum systems and the black hole interior in holographic duality

In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. This identification still has many puzzles, including the boundary descriptions of the event horizons, the interiors of the black hole, and the singularities. Compounding these mysteries is the fact that, while there is no interaction between the CFTs, observers from them can fall into the black hole and interact. We will address these issues in this talk. In particular, we (i) present a boundary formulation of infalling observers; (ii) show that in any holographic systems, a sharp event horizon can only emerge in the infinite N limit; (iii) give an explicit construction in the boundary theory of an evolution operator for a family of bulk in-falling observers, making manifest the boundary emergence of the black hole horizons, the interiors, and the associated causal structure.
A by-product is a concept called causal connectability, which is a criterion for any two quantum systems (which do not necessarily have a known gravity dual) to have an emergent sharp horizon structure.