Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the N = 6 solution

He, Temple; Hubeny, Veronika E.; Rota, Massimiliano

doi:10.1007/JHEP06(2025)055

Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the N = 6 solution

Journal Article · Thu Jun 05 00:00:00 EDT 2025 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP06(2025)055· OSTI ID:3006016

^[1]; ^[2]; ^[3]

California Institute of Technology (CalTech), Pasadena, CA (United States)
Univ. of California, Davis, CA (United States)
Univ. of California, Davis, CA (United States); Univ. of Bristol (United Kingdom)

We compute the set of all extreme rays of the 6-party subadditivity cone that are compatible with strong subadditivity. In total, we identify 208 new (genuine 6-party) orbits, 52 of which violate at least one known holographic entropy inequality. For the remaining 156 orbits, which do not violate any such inequalities, we construct holographic graph models for 150 of them. For the final 6 orbits, it remains an open question whether they are holographic. Consistent with the strong form of the conjecture in [1], 148 of these graph models are trees. However, 2 of the graphs contain a “bulk cycle”, leaving open the question of whether equivalent models with tree topology exist, or if these extreme rays are counterexamples to the conjecture. The paper includes a detailed description of the algorithm used for the computation, which is presented in a general framework and can be applied to any situation involving a polyhedral cone defined by a set of linear inequalities and a partial order among them to find extreme rays corresponding to down-sets in this poset.

View Accepted Manuscript (DOE)

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0009999; SC0011632

OSTI ID:: 3006016

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 6 Vol. 2025; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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