Upper bound of holographic entanglement entropy combinations

TL;DR

This paper develops a formalism to evaluate upper bounds of holographic entanglement entropy combinations, revealing insights into multipartite entanglement structures across various dimensions in holography.

Contribution

It introduces a systematic method to classify and compute upper bounds of entropy combinations, advancing understanding of entanglement structures in holographic theories.

Findings

Derived formulas for upper bounds in different dimensions

Classified configurations of entropy combinations

Revealed dimension-dependent entanglement structures

Abstract

In this work, we develop a systematic formalism to evaluate the upper bound of a large family of holographic entanglement entropy combinations when fixing $n$ subsystems and fine-tuning one other subsystem. The upper bound configurations and values of these entropy combinations can be derived and classified. The upper bound of these entropy combinations reveals holographic $n+1$-partite entanglement that $n$ fixed subsystems participate in. In AdS$_3$/CFT$_2$, AdS$_4$/CFT$_3$, and even higher-dimensional holography, one can, in principle, find different formulas of upper bound values, reflecting the fundamental difference in entanglement structure in different dimensions.