Topological Einstein gravity as Kodaira-Spencer gravity
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908690161860608 |
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| author | Erdmenger, Johanna Karl, Jonathan Kastikainen, Jani Meyer, René Scheppach, Henri |
| author_facet | Erdmenger, Johanna Karl, Jonathan Kastikainen, Jani Meyer, René Scheppach, Henri |
| contents | As a contribution towards quantizing three-dimensional gravity, we show at the classical level that Euclidean three-dimensional Einstein gravity with a negative cosmological constant is uplifted to the $SU(2)$-invariant sector of Kodaira-Spencer gravity on a Calabi-Yau three-fold. Kodaira-Spencer gravity appears in the target space description of the B-model topological string theory and describes deformations of a complex structure. We prove that given a reference solution of Einstein gravity in the first-order formulation, a second off-shell configuration uplifts to a unique complex structure deformation in six dimensions. If the configuration satisfies Einstein's equations, the complex structure deformation is integrable, i.e. a solution of Kodaira-Spencer gravity. We demonstrate the uplift explicitly for Bañados solutions. Our construction embeds three-dimensional gravity into topological string theory and AdS$_3$/CFT$_2$ duality into twisted holography. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Einstein gravity as Kodaira-Spencer gravity Erdmenger, Johanna Karl, Jonathan Kastikainen, Jani Meyer, René Scheppach, Henri High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics As a contribution towards quantizing three-dimensional gravity, we show at the classical level that Euclidean three-dimensional Einstein gravity with a negative cosmological constant is uplifted to the $SU(2)$-invariant sector of Kodaira-Spencer gravity on a Calabi-Yau three-fold. Kodaira-Spencer gravity appears in the target space description of the B-model topological string theory and describes deformations of a complex structure. We prove that given a reference solution of Einstein gravity in the first-order formulation, a second off-shell configuration uplifts to a unique complex structure deformation in six dimensions. If the configuration satisfies Einstein's equations, the complex structure deformation is integrable, i.e. a solution of Kodaira-Spencer gravity. We demonstrate the uplift explicitly for Bañados solutions. Our construction embeds three-dimensional gravity into topological string theory and AdS$_3$/CFT$_2$ duality into twisted holography. |
| title | Topological Einstein gravity as Kodaira-Spencer gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2512.03142 |