{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-holographic-entropy-cone-for-five-regions","title":"The Holographic Entropy Cone for Five Regions","arxiv_id":"1903.09148","date":"2019-03-21","proceeding":null,"authors":["Sergio Hernández-Cuenca"],"abstract":"Even though little is known about the quantum entropy cone for $N\\geq4$ subsystems, holographic techniques allow one to get a handle on the subspace of entropy vectors corresponding to states with gravity duals. For static spacetimes and $N$ boundary subsystems, this space is a convex polyhedral cone known as the holographic entropy cone $\\mathcal{C}_N$ for $N$ regions. While an explicit description of $\\mathcal{C}_N$ was accomplished for all $N\\leq4$ in the initial study, the information given about larger $N$ was only partial already for $\\mathcal{C}_5$. This letter provides a complete construction of $\\mathcal{C}_5$ by exhibiting graph models for every extreme ray orbit generating the cone defined by all proven holographic entropy inequalities for $N=5$. The question of whether there exist additional inequalities for $5$ parties is thus settled with a negative answer. The conjecture that $\\mathcal{C}_5$ coincides with the analogous cone for dynamical spacetimes is supported by demonstrating that the information quantities defining its facets are primitive.","url_abs":"http://arxiv.org/abs/1903.09148v3","url_pdf":"http://arxiv.org/pdf/1903.09148v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-holographic-entropy-cone-for-five-regions","repo_url":"https://github.com/SergioHC95/Holographic-Entropy-Cone","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}