Journal Article

Towards a complete classification of holographic entropy inequalities

Furuya, Keiichiro, Naskar, Joydeep, Bao, Ning

2025

Overview

A bstract We propose a deterministic method to find all holographic entropy inequalities that have corresponding contraction maps and argue the completeness of our method. We use a triality between holographic entropy inequalities, contraction maps and partial cubes. More specifically, the validity of a holographic entropy inequality is implied by the existence of a contraction map, which we prove to be equivalent to finding an isometric embedding of a contracted graph. Thus, by virtue of the argued completeness of the contraction map proof method, the problem of finding all holographic entropy inequalities is equivalent to the problem of finding all contraction maps, which we translate to a problem of finding all image graph partial cubes. We give an algorithmic solution to this problem and characterize the complexity of our method. We also demonstrate interesting by-products, most notably, a procedure to generate candidate quantum entropy inequalities.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
• Subject: AdS-CFT Correspondence / Algorithms / Algorithms and Theoretical Developments / Classical and Quantum Gravitation / Classification / Completeness / Cubes / Elementary Particles / Entropy / Equivalence / High energy physics / Holography / Inequalities / Models of Quantum Gravity / Physics / Physics and Astronomy / Quantum Field Theories / Quantum Field Theory / Quantum Physics / Regular Article - Theoretical Physics / Relativity Theory / String Theory