Holographic Cone of Average Entropies

TL;DR

This paper extends the concept of the holographic entropy cone to average entropies of p-partite subsystems for any number of regions, conjecturing a simplicial structure with specific inequalities and linking extreme rays to black hole evaporation stages.

Contribution

It introduces a new framework for analyzing average entropies in holography, conjectures the cone’s simplicial nature, and characterizes its extreme rays related to black hole physics.

Findings

Conjecture that the holographic cone of average entropies is simplicial.

Specification of all bounding inequalities for the cone.

Identification of extreme rays related to black hole evaporation stages.

Abstract

The holographic entropy cone identifies entanglement entropies of field theory regions, which are consistent with representing semiclassical spacetimes under gauge/gravity duality; it is currently known up to 5 regions. We point out that average entropies of p-partite subsystems can be similarly analyzed for arbitrarily many regions. We conjecture that the holographic cone of average entropies is simplicial and specify all its bounding inequalities. Its extreme rays combine features of bipartite and perfect tensor entanglement, and correspond to stages of unitary evaporation of old black holes.