AI 中文总结
该研究通过6D Kodaira-Spencer引力的维数约化，从其复共轭拷贝导出完整3D Einstein作用量，为将3D引力欧几里得路径积分嵌入拓扑弦理论提供关键步骤。
AI 中文摘要
为将3D引力嵌入拓扑弦理论，我们证明6D Kodaira-Spencer引力在$\text{AdS}_3\times S^3$上的维数约化（即扭曲全息论的低能描述）包含一个子区域，该区域与$\text{AdS}_3$上的手征3D引力作用量一致。此外，我们证明完整的3D Einstein作用量是6D Kodaira-Spencer引力的两个独立复共轭拷贝约化得到的。我们在经典作用量层面明确进行了维数约化，扩展了我们之前将两种理论的运动方程关联起来的工作。我们的约化过程基于对非局域的6D Kodaira-Spencer作用量的新颖重写，将其改写为规范群$\text{SL}(2,\boldsymbol{\text{C}})$的局域6D全纯Chern-Simons作用量，该作用量在我们确定的复结构形变的子区域内有效。我们的结果为将3D引力的欧几里得路径积分嵌入拓扑弦理论提供了必要的一步。
英文摘要
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.
Comments47 pages, 5 appendices
