Entropic Interpretation of Einstein Equation in dS/CFT
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915639849910272 |
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| author | Fujiki, Kosei Kohara, Michitaka Shinmyo, Kotaro Suzuki, Yu-ki Takayanagi, Tadashi |
| author_facet | Fujiki, Kosei Kohara, Michitaka Shinmyo, Kotaro Suzuki, Yu-ki Takayanagi, Tadashi |
| contents | In this paper, we demonstrate that the first law of holographic pseudo-entropy, which is a non-Hermitian generalization of entanglement entropy in a two-dimensional conformal field theory (CFT), is equivalent to the perturbative Einstein equation in three-dimensional de Sitter (dS) space, assuming the dS/CFT correspondence. Our analysis reveals that the geodesic that accurately satisfies the first law of holographic pseudo-entropy consists of a timelike curve and a curve whose coordinates are complex. We also demonstrate that infinitesimal changes to the pseudo entropy satisfy a Klein-Gordon equation in two-dimensional de Sitter space. These imply the emergence of a time coordinate from a Euclidean CFT in dS/CFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07915 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropic Interpretation of Einstein Equation in dS/CFT Fujiki, Kosei Kohara, Michitaka Shinmyo, Kotaro Suzuki, Yu-ki Takayanagi, Tadashi High Energy Physics - Theory General Relativity and Quantum Cosmology In this paper, we demonstrate that the first law of holographic pseudo-entropy, which is a non-Hermitian generalization of entanglement entropy in a two-dimensional conformal field theory (CFT), is equivalent to the perturbative Einstein equation in three-dimensional de Sitter (dS) space, assuming the dS/CFT correspondence. Our analysis reveals that the geodesic that accurately satisfies the first law of holographic pseudo-entropy consists of a timelike curve and a curve whose coordinates are complex. We also demonstrate that infinitesimal changes to the pseudo entropy satisfy a Klein-Gordon equation in two-dimensional de Sitter space. These imply the emergence of a time coordinate from a Euclidean CFT in dS/CFT. |
| title | Entropic Interpretation of Einstein Equation in dS/CFT |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2511.07915 |