Handlebody phases and the polyhedrality of the holographic entropy cone

Understand

The notion of a holographic entropy cone has recently been introduced and it has been proven that this cone is polyhedral.

• However, the original definition was fully geometric and did not strictly require a holographic duality.
• We introduce a new definition of the cone, insisting that the geometries used for its construction should be dual to states of a CFT.
• As a result, the polyhedrality of this holographic cone does not immediately follow.