SciPost Submission Page
A new characterization of the holographic entropy cone
by Guglielmo Grimaldi, Matthew Headrick, Veronika E. Hubeny
Submission summary
| Authors (as registered SciPost users): | Guglielmo Grimaldi |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202601_00078v1 (pdf) |
| Date submitted: | Jan. 31, 2026, 3:32 p.m. |
| Submitted by: | Guglielmo Grimaldi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Entanglement entropies computed using the holographic Ryu-Takayanagi formula are known to obey an infinite set of linear inequalities, which define the so-called RT entropy cone. The general structure of this cone, or equivalently the set of all valid inequalities, is unknown. It is also unknown whether those same inequalities are also obeyed by entropies computed using the covariant Hubeny-Rangamani-Takayanagi formula, although significant evidence has accumulated that they are. Using Markov states, we develop a test of this conjecture in a heretofore unexplored regime. The test reduces to checking that a given inequality obeys a certain majorization property, which is easy to evaluate. We find that the RT inequalities pass this test and, surprisingly, only such inequalities do so. Our results not only provide strong new evidence that the HRT and RT cones coincide, but also offer a completely new characterization of that cone.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report #1 by Ning Bao (Referee 1) on 2026-2-5 (Invited Report)
Strengths
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Is a novel and interesting expansion of techniques developed for studying holographic entanglement entropy inequalities.
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Points to potential new ways forward in understanding and categorizing the inequalities, in particular as it relates to their veracity in time-dependent situations.
Weaknesses
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One of the main results is only conjectural, though this is addressed in follow-up work.
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Unclear whether this will actually help give physical interpretations to the meanings of the holographic entanglement entropy inequalities; has the potential to be a bit formalism for its own sake.
Report
It would be interesting to see what subset of the results could be proven using contraction map techniques alone, without appeal to majorization/null reduction, and what subset require these new techniques to function.
Requested changes
- I would appreciate an expanded discussion of potential physical consequences of the majorization/null reduction aspect, aside from its potential relation to proving that these inequalities are true for time dependent geometries. In particular, I would like to see an answer to the question of what impact, if any, holographic entanglement inequalities beyond SA and MMI have had on holography for people who don't care about the inequalities for their own sake. I feel that such contextualization is necessary to prevent the field from becoming epicyclic.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)