Event

In the AdS/CFT correspondence, if a CFT state is dual to a semiclassical spacetime, its entanglement entropies (minimal surface areas) must obey certain inequalities. The best-known examples are the strong subadditivity of entanglement entropy (SSA) and the monogamy of mutual information (MMI). Together, such inequalities define the so-called holographic entropy cone. It is an interesting object because (a) it quantifies what is special about holography--how holographic CFTs are different from general quantum mechanical systems, and (b) it highlights special entanglement structures (bipartite, perfect tensor), which are the atomic ingredients for building up holographic spacetimes.

The holographic entropy cone for static states is known (modulo a few conjectured inequalities), but it is not known for time-dependent states. Is it possible to use time dependence to construct more general bulk spacetimes, which violate conditions that hold in static geometries? I will show that this does not happen in the AdS3/CFT2 correspondence. The argument has many interesting aspects: (1) it completely dispenses with any notion of a bulk slice and operates directly in kinematic space (space of CFT intervals); (2) it provides hints for how to prove the remaining, conjectured inequalities; (3) it reduces to repeated applications of the strong subadditivity of entanglement entropy. I hope we will discuss the significance of these facts together.