Year: 2026
Type: preprint
Abstract: In view of embedding 3D gravity into topological string theory, we show that the dimensional reduction of 6D Kodaira-Spencer gravity on $\text{AdS}_3\times S^3$, i.e. the low-energy description of twisted holography, contains a subsector that coincides with the action of chiral 3D gravity on $\text{AdS}_3$. Furthermore, we show that the full 3D Einstein action is obtained as the reduction of two independent complex-conjugate copies of 6D Kodaira-Spencer gravity. We perform the dimensional reduction explicitly at the level of the classical actions, extending our previous work that related the equations of motion of the two theories. Our reduction procedure is based on a novel rewriting of the non-local 6D Kodaira-Spencer action as a local 6D holomorphic Chern-Simons action for the gauge group $\mathrm{SL}(2,\mathbb{C})$, valid within a subsector of complex structure deformations that we identify. Our results provide a necessary step toward embedding the Euclidean path integral of 3D gravity into topological string theory.
Source: arXiv (Cornell University)
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7203899017
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