How Einstein's Equation Emerges From CFT$_2$
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912681726836736 |
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| author | Jiang, Xin Wang, Peng Wu, Houwen Yang, Haitang |
| author_facet | Jiang, Xin Wang, Peng Wu, Houwen Yang, Haitang |
| contents | The {\it finiteness} of the entanglement entropies between disjoint subsystems enables us to show that, the dynamical equation of the entanglement entropy in CFT$_2$ is precisely three dimensional Einstein's equation. We establish a profound relation between the cosmological constant and CFT$_2$ entanglement entropy. Thus entanglement entropies induce internal gravitational geometries in CFT$_2$. Extracting the dual metric from an entanglement entropy becomes a straightforward procedure. Remarkably, we discover that the renormalization group equation is a geometric identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19711 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How Einstein's Equation Emerges From CFT$_2$ Jiang, Xin Wang, Peng Wu, Houwen Yang, Haitang High Energy Physics - Theory The {\it finiteness} of the entanglement entropies between disjoint subsystems enables us to show that, the dynamical equation of the entanglement entropy in CFT$_2$ is precisely three dimensional Einstein's equation. We establish a profound relation between the cosmological constant and CFT$_2$ entanglement entropy. Thus entanglement entropies induce internal gravitational geometries in CFT$_2$. Extracting the dual metric from an entanglement entropy becomes a straightforward procedure. Remarkably, we discover that the renormalization group equation is a geometric identity. |
| title | How Einstein's Equation Emerges From CFT$_2$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.19711 |