Holographic entropy cone for five regions

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 CN for N regions. While an explicit description of CN was accomplished for all N≤4 in the initial study, the information given about larger N was only partial already for C5. This paper 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 five parties is thus settled with a negative answer. The conjecture that C5 coincides with the analogous cone for dynamical spacetimes is also supported by demonstrating that the information quantities defining its facets are primitive.