Nesting is not contracting
Abstract The default way of proving holographic entropy inequalities is the contraction method. It divides Ryu-Takayanagi (RT) surfaces on the ‘greater than’ side of the inequality into segments, then glues the segments into candidate RT surfaces for terms on the ‘less than’ side. Here we discuss ho...
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SpringerOpen
2025-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP06(2025)122 |
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| author | Bartłomiej Czech Sirui Shuai |
| author_facet | Bartłomiej Czech Sirui Shuai |
| author_sort | Bartłomiej Czech |
| collection | DOAJ |
| description | Abstract The default way of proving holographic entropy inequalities is the contraction method. It divides Ryu-Takayanagi (RT) surfaces on the ‘greater than’ side of the inequality into segments, then glues the segments into candidate RT surfaces for terms on the ‘less than’ side. Here we discuss how proofs by contraction are constrained and informed by entanglement wedge nesting (EWN)—the property that enlarging a boundary region can only enlarge its entanglement wedge. We propose that: (i) all proofs by contraction necessarily involve candidate RT surfaces, which violate EWN; (ii) violations of EWN in contraction proofs of maximally tight inequalities occur commonly and — where this can be quantified — with maximal density near boundary conditions; (iii) the non-uniqueness of proofs by contraction reflects inequivalent ways of violating EWN. As evidence and illustration, we study the recently discovered infinite families of holographic entropy inequalities, which are associated with tessellations of the torus and the projective plane. We explain the logic, which underlies their proofs by contraction. We find that all salient aspects of the requisite contraction maps are dictated by EWN while all their variable aspects set the scheme for how to violate EWN. We comment on whether the tension between EWN and contraction maps might help in characterizing maximally tight holographic entropy inequalities. |
| format | Article |
| id | doaj-art-065c263e99c6465b83f7bea3362cdd31 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-065c263e99c6465b83f7bea3362cdd312025-08-20T03:42:43ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025614510.1007/JHEP06(2025)122Nesting is not contractingBartłomiej Czech0Sirui Shuai1Institute for Advanced Study, Tsinghua UniversityInstitute for Advanced Study, Tsinghua UniversityAbstract The default way of proving holographic entropy inequalities is the contraction method. It divides Ryu-Takayanagi (RT) surfaces on the ‘greater than’ side of the inequality into segments, then glues the segments into candidate RT surfaces for terms on the ‘less than’ side. Here we discuss how proofs by contraction are constrained and informed by entanglement wedge nesting (EWN)—the property that enlarging a boundary region can only enlarge its entanglement wedge. We propose that: (i) all proofs by contraction necessarily involve candidate RT surfaces, which violate EWN; (ii) violations of EWN in contraction proofs of maximally tight inequalities occur commonly and — where this can be quantified — with maximal density near boundary conditions; (iii) the non-uniqueness of proofs by contraction reflects inequivalent ways of violating EWN. As evidence and illustration, we study the recently discovered infinite families of holographic entropy inequalities, which are associated with tessellations of the torus and the projective plane. We explain the logic, which underlies their proofs by contraction. We find that all salient aspects of the requisite contraction maps are dictated by EWN while all their variable aspects set the scheme for how to violate EWN. We comment on whether the tension between EWN and contraction maps might help in characterizing maximally tight holographic entropy inequalities.https://doi.org/10.1007/JHEP06(2025)122AdS-CFT CorrespondenceGauge-Gravity Correspondence |
| spellingShingle | Bartłomiej Czech Sirui Shuai Nesting is not contracting Journal of High Energy Physics AdS-CFT Correspondence Gauge-Gravity Correspondence |
| title | Nesting is not contracting |
| title_full | Nesting is not contracting |
| title_fullStr | Nesting is not contracting |
| title_full_unstemmed | Nesting is not contracting |
| title_short | Nesting is not contracting |
| title_sort | nesting is not contracting |
| topic | AdS-CFT Correspondence Gauge-Gravity Correspondence |
| url | https://doi.org/10.1007/JHEP06(2025)122 |
| work_keys_str_mv | AT bartłomiejczech nestingisnotcontracting AT siruishuai nestingisnotcontracting |