Papers › The Holographic Entropy Cone for Five Regions
The Holographic Entropy Cone for Five Regions
Sergio Hernández-Cuenca
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Even though little is known about the quantum entropy cone for N≥4 subsystems, holographic techniques allow one to get a handle on the subspace of entropy vectors corresponding to states with gravity duals. For static spacetimes and N boundary subsystems, this space is a convex polyhedral cone known as the holographic entropy cone 𝒞_N for N regions. While an explicit description of 𝒞_N was accomplished for all N≤4 in the initial study, the information given about larger N was only partial already for 𝒞₅. This letter provides a complete construction of 𝒞₅ by exhibiting graph models for every extreme ray orbit generating the cone defined by all proven holographic entropy inequalities for N=5. The question of whether there exist additional inequalities for $5$ parties is thus settled with a negative answer. The conjecture that 𝒞₅ coincides with the analogous cone for dynamical spacetimes is supported by demonstrating that the information quantities defining its facets are primitive.
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