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<p>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<sub>3</sub>/CFT<sub>2</sub> duality into twisted holography.</p>

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Topological Einstein gravity as Kodaira-Spencer gravity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月7日

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  • Johanna Erdmenger,
  • Jonathan Karl,
  • Jani Kastikainen,
  • René Meyer,
  • Henri Scheppach

摘要

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 AdS3/CFT2 duality into twisted holography.