We describe the coupling of holomorphic Chern–Simons theory at large $N$ with Kodaira–Spencer gravity. We explain a new anomaly cancellation mechanism at all loops in perturbation theory for open-closed topological $B$‑model. At one loop this anomaly cancellation is analogous to the Green–Schwarz mechanism. As an application, we introduce a type I version of Kodaira–Spencer theory in complex dimensions $3$ and $5$. In complex dimension $5$, we show that it can only be coupled consistently at the quantum level to holomorphic Chern–Simons theory with gauge group $SO(32)$. This is analogous to the Green–Schwarz mechanism for the physical type I string. This coupled system is conjectured to be a supersymmetric localization of type I string theory. In complex dimension 3, the required gauge group is $SO(8)$.

中文翻译：

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拓扑字符串中的异常消除

我们描述了大 $N$ 的全纯陈-西蒙斯理论与 Kodaira-Spencer 引力的耦合。我们在微扰理论中为开闭拓扑 $B$ 模型在所有循环中解释了一种新的异常消除机制。在一个循环中，这种异常消除类似于 Green-Schwarz 机制。作为一个应用程序，我们在复杂维度 $3$ 和 $5$ 中引入了 Kodaira-Spencer 理论的 I 类版本。在复维 $5$ 中，我们表明它只能在量子水平上与规范群 $SO(32)$ 的全纯陈-西蒙斯理论一致地耦合。这类似于物理类型 I 弦的 Green-Schwarz 机制。这个耦合系统被推测为 I 型弦理论的超对称局域化。在复维 3 中，所需的规范组是 $SO(8)$。