拓扑递归与Gromov--Witten理论中的Conifold分解
Conifold factorization in topological recursion and Gromov--Witten theory
浏览论文内容
中文总结 AI 辅助
本文证明了谱曲线正则节点退化下拓扑递归的分解定理，将配分函数分解为归一化部分、高斯真空和连通图求和，恢复了conifold间隙，并给出了局部$\mathbb P^2$、$\mathbb F_0$和$\mathbb F_1$的Gromov--Witten分解实例。
中文摘要 AI 辅助
我们证明了在谱曲线的正则节点退化附近，允许对数谱坐标的普通拓扑递归的分解定理。闭亏格$g\ge2$的配分函数分解为归一化的配分函数、一个普适的高斯真空以及一个连通图求和的指数。该图求和在消失周期中具有严格正阶，因此该分解恢复了conifold间隙，将消失周期中零阶项与归一化的自由能等同，并为周期的正幂系数给出了有限图公式。在固定亏格下，正则级数在周期和沿节点轨迹的参数上联合收敛。高斯颈张量可以用参数化$\mathbb P^1$的相对Gromov--Witten不变量来表示。作为例子，我们使用重构方法在conifold框架下获得了局部$\mathbb P^2$和局部$\mathbb F_0$的Gromov--Witten分解，其背景分别为$\mathbb C^3$和已解conifold。类似的局部$\mathbb F_1$分解的背景是$\mathbb P^1$上的$\mathcal O(1)\oplus\mathcal O(-3)$。
英文摘要
We prove a factorization theorem for ordinary topological recursion near a regular nodal degeneration of a spectral curve, allowing logarithmic spectral coordinates. The partition function for closed genera $g\ge2$ factors into the partition function of the normalization, a universal Gaussian vacuum, and the exponential of a connected graph sum. This graph sum has strictly positive order in the vanishing period, and thus the factorization recovers the conifold gap, identifies the term of degree zero in the vanishing period with the free energy of the normalization, and gives finite graph formulas for the coefficients of positive powers of the period. At fixed genus, the regular series converges jointly in the period and the parameters along the nodal locus. The Gaussian neck tensors can be expressed in terms of relative Gromov--Witten invariants of a parametrized $\mathbb P^1$. As examples, we use remodeling to obtain Gromov--Witten factorizations for local $\mathbb P^2$ and local $\mathbb F_0$ in the conifold frame, with backgrounds $\mathbb C^3$ and the resolved conifold, respectively. The analogous local $\mathbb F_1$ factorization has background $\mathcal O(1)\oplus\mathcal O(-3)$ over $\mathbb P^1$.
发表机构
- Tsinghua University（清华大学）
- Peking University（北京大学）
机构由 AI 辅助整理，请以论文原文为准。
