Topological Einstein gravity as Kodaira-Spencer gravity
Abstract
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 -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 Ba\~nados solutions. Our construction embeds three-dimensional gravity into topological string theory and AdS/CFT duality into twisted holography.
Cite
@article{arxiv.2512.03142,
title = {Topological Einstein gravity as Kodaira-Spencer gravity},
author = {Johanna Erdmenger and Jonathan Karl and Jani Kastikainen and René Meyer and Henri Scheppach},
journal= {arXiv preprint arXiv:2512.03142},
year = {2025}
}
Comments
56 pages, 1 figure, 6 appendices