The Holographic Entropy Cone for Five Regions

Sergio Hernández-Cuenca

doi:10.1103/PhysRevD.100.026004

paper

The Holographic Entropy Cone for Five Regions

arXiv:1903.09148 · doi:10.1103/PhysRevD.100.026004

Abstract

Even though little is known about the quantum entropy cone for $N \geq 4$ 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 $N \leq 4$ in the initial study, the information given about larger $N$ was only partial already for $C_{5}$ . This letter provides a complete construction of $C_{5}$ 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 $C_{5}$ coincides with the analogous cone for dynamical spacetimes is supported by demonstrating that the information quantities defining its facets are primitive.

8 pages, 19 graphs; v2: minor changes, references added, comments about six regions revised and a new inequality included; v3: essentially matches published version

The Holographic Entropy Cone for Five Regions

Abstract

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