Non-linear Holographic Entanglement Entropy Inequalities for Single Boundary 2D CFT

TL;DR

This paper derives four new non-linear entanglement entropy inequalities for a single boundary 2D CFT in a holographic setting, expanding understanding of holographic entropy constraints beyond known linear inequalities.

Contribution

It introduces four novel non-linear entropy inequalities and an equality for a 2D CFT, based on strong subadditivity and geometric theorems, specific to single boundary holographic systems.

Findings

Four new non-linear entropy inequalities derived.

An equality from hyperbolic Ptolemy's theorem established.

Enhanced understanding of holographic entropy constraints.

Abstract

Significant work has gone into determining the minimal set of entropy inequalities that determine the holographic entropy cone. Holographic systems with three or more parties have been shown to obey additional inequalities that generic quantum systems do not. We consider a two dimensional conformal field theory that is a single boundary of a holographic system and find four additional non-linear inequalities which are derived from strong subadditivity and the formula for the entanglement entropy of a region on the conformal field theory. We also present an equality obtained by application of a hyperbolic extension of Ptolemy's theorem to a two dimensional conformal field theory.