A holographic inequality for $N=7$ regions

TL;DR

This paper introduces a new holographic entropy inequality involving seven regions, extending known constraints and supporting conjectures about the structure of holographic inequalities in quantum gravity.

Contribution

The authors derive a novel inequality for seven disjoint regions in holographic duality, expanding the understanding of entropy constraints beyond previous limits.

Findings

New inequality involving 7 regions supports conjectured structure

Extends known entropy inequalities from 5 to 7 regions

Provides a framework for future searches of holographic inequalities

Abstract

In holographic duality, boundary states that have semiclassical bulk duals must obey inequalities, which bound their subsystems' von Neumann entropies. Hitherto known inequalities constrain entropies of reduced states on up to $N=5$ disjoint subsystems. Here we report one new such inequality, which involves $N=7$ disjoint regions. Our work supports a recent conjecture on the structure of holographic inequalities, which predicted the existence and schematic form of the new inequality. We explain the logic and educated guesses by which we arrived at the inequality, and comment on the feasibility of employing similar tactics in a more exhaustive search.