有限N矩阵模型中的广中几何与复兴理论
Hironaka Geometry and Resurgence in Finite-$N$ Matrix Models
- School of Science, Huzhou Normal University（湖州师范学院理学院）
- Mandelstam Institute for Theoretical Physics, School of Physics, University of the Witwatersrand（威特沃特斯兰德大学物理学院曼德尔斯坦理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
该研究通过广中分解揭示有限N矩阵模型的非微扰结构，找到产生额外鞍点的分歧点，证明特定鞍点主导微扰论奇点与增长，建立了有限N不变量几何与复兴理论的联系。
中文摘要 AI 辅助
我们研究有限N不变量理论如何组织矩阵模型的非微扰结构。对于4个无迹2×2埃尔米特矩阵的模型，广中分解（Hironaka decomposition）将规范不变构型空间实现为初等不变量空间的8叶分支覆盖。我们证明，当作用量仅依赖于初等不变量时，该覆盖的分歧点会自然产生额外的鞍点。对于一个显式的秩2鞍点，我们计算其作用量、单圈归一化以及与微扰真空的皮卡-勒夫谢茨（Picard-Lefschetz）联系。该鞍点主导了微扰论的主导玻雷尔奇点和大阶增长，而其首次涨落修正无需拟合参数即可重现首次次主导大阶修正。我们的结果为有限N不变量几何与矩阵模型复兴理论建立了具体联系。
英文摘要
We study how finite-$N$ invariant theory organizes the non-perturbative structure of matrix models. For a model of four traceless Hermitian $2\times 2$ matrices, the Hironaka decomposition realizes the gauge-invariant configuration space as an eight-sheeted branched cover of the space of primary invariants. We show that ramification points of this cover naturally generate additional saddle points when the action depends only on the primaries. For an explicit rank-two saddle, we compute its action, one-loop normalization and Picard--Lefschetz connection to the perturbative vacuum. The same saddle controls the leading Borel singularity and large-order growth of perturbation theory, while its first fluctuation correction reproduces the first subleading large-order correction with no fitted parameters. Our results provide a concrete link between finite-$N$ invariant geometry and resurgence in matrix models.
