Minimax surfaces and the holographic entropy cone
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913839603253248 |
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| author | Grado-White, Brianna Grimaldi, Guglielmo Headrick, Matthew Hubeny, Veronika E. |
| author_facet | Grado-White, Brianna Grimaldi, Guglielmo Headrick, Matthew Hubeny, Veronika E. |
| contents | We study and prove properties of the minimax formulation of the HRT holographic entanglement entropy formula, which involves finding the maximal-area surface on a timelike hypersurface, or time-sheet, and then minimizing over the choice of time-sheet. In this formulation, the homology condition is imposed at the level of the spacetime: the homology regions are spacetime volumes rather spatial regions. We show in particular that the smallest minimax homology region is the entanglement wedge. The minimax prescription suggests a way to construct a graph model for time-dependent states, a weighted graph on which min cuts compute HRT entropies. The existence of a graph model would imply that HRT entropies obey the same inequalities as RT entropies, in other words that the RT and HRT entropy cones coincide. Our construction of a graph model relies on the time-sheets obeying a certain ``cooperating'' property, which we show holds in some examples and for which we give a partial proof; however, we also find scenarios where it may fail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09894 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimax surfaces and the holographic entropy cone Grado-White, Brianna Grimaldi, Guglielmo Headrick, Matthew Hubeny, Veronika E. High Energy Physics - Theory General Relativity and Quantum Cosmology We study and prove properties of the minimax formulation of the HRT holographic entanglement entropy formula, which involves finding the maximal-area surface on a timelike hypersurface, or time-sheet, and then minimizing over the choice of time-sheet. In this formulation, the homology condition is imposed at the level of the spacetime: the homology regions are spacetime volumes rather spatial regions. We show in particular that the smallest minimax homology region is the entanglement wedge. The minimax prescription suggests a way to construct a graph model for time-dependent states, a weighted graph on which min cuts compute HRT entropies. The existence of a graph model would imply that HRT entropies obey the same inequalities as RT entropies, in other words that the RT and HRT entropy cones coincide. Our construction of a graph model relies on the time-sheets obeying a certain ``cooperating'' property, which we show holds in some examples and for which we give a partial proof; however, we also find scenarios where it may fail. |
| title | Minimax surfaces and the holographic entropy cone |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2502.09894 |