Superbalance of Holographic Entropy Inequalities

Abstract

The domain of allowed von Neumann entropies of a holographic field theory carves out a polyhedral cone -- the holographic entropy cone -- in entropy space. Such polyhedral cones are characterized by their extreme rays. For an arbitrary number of parties, it is known that the so-called perfect tensors are extreme rays. In this work, we constrain the form of the remaining extreme rays by showing that they correspond to geometries with vanishing mutual information between any two parties, ensuring the absence of Bell pair type entanglement between them. This is tantamount to proving that besides subadditivity, all non-redundant holographic entropy inequalities are superbalanced, i.e. not only do UV divergences cancel in the inequality itself (assuming smooth entangling surfaces), but also in the purification thereof.

arXiv comment21 pages, 6 figures; v2: Minor clarification comments, version to appear in JHEP

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• Holographic Entropy Inequalities and Multipartite Entanglement
• The Symmetrized Holographic Entropy Cone
• Holographic Cone of Average Entropies
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• Two infinite families of facets of the holographic entropy cone
• Perfect tensor hyperthreads
• Testing holographic entropy inequalities in 2+1 dimensions
• Towards a complete classification of holographic entropy inequalities
• More on the upper bound of holographic n-partite information
• A gap between holographic and quantum mechanical extreme rays of the subadditivity cone
• A framework for generalizing toric inequalities for holographic entanglement entropy
• Multipartite Optimized Correlation Measures and Holography
• Beyond the Holographic Entropy Cone via Cycle Flows
• Purely GHZ-like entanglement is forbidden in holography
• Upper bound of holographic entanglement entropy combinations
• Cluster algebraic description of entanglement patterns for the BTZ black hole
• Exploring the holographic entropy cone via reinforcement learning
• Topological entanglement entropy meets holographic entropy inequalities