非临界M理论及解锥形：细化与非微扰完备化
Non-critical M-Theory and the Resolved Conifold: Refinement and Nonperturbative Completion
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中文总结 AI 辅助
本文推广非临界M理论与解锥形A模型的对应至细化理论，通过旋转真空巨势匹配细化Gopakumar--Vafa展开，并精确对应非微扰完备化，为这些完备化提供微观谱实现。
中文摘要 AI 辅助
我们将Hořava--Keeler关于有限温度非临界M理论与解锥形A模型之间的对应关系推广到细化理论。稳态旋转非临界M理论真空的巨势重现了细化的Gopakumar--Vafa展开，其中角化学势使$\Omega$-背景偏离自对偶点$\eps_1=-\eps_2$。在有限热半径下，我们建立了与Hattab--Palti和Chuang分别提出的非微扰锥形完备化的精确匹配，前者针对未细化情形，后者针对细化情形。单粒子Schwinger被积函数及其积分环路均源自非临界M理论谱和预解式，为这些完备化提供了微观谱实现。该对应关系确定了非恒定BPS扇区和三次局域贡献，而剩余的多项式模糊性及与模无关的常数映射扇区需要单独归一化。我们解释了为何解锥形的单一原始无自旋多重态使这一识别成为可能，并讨论了扩展到更一般局部Calabi--Yau几何所需的额外电荷和自旋相关微观数据。
英文摘要
We extend the Hořava--Keeler correspondence between finite-temperature non-critical M-theory and the resolved-conifold A-model to the refined theory. The grand potential of the stationary rotating non-critical M-theory vacuum reproduces the refined Gopakumar--Vafa expansion, with the angular chemical potential deforming the $Ω$-background away from the self-dual locus $\eps_1=-\eps_2$. At finite thermal radius, we establish an exact match with the nonperturbative conifold completions proposed by Hattab--Palti and by Chuang in the unrefined and refined cases, respectively. Both the one-particle Schwinger integrand and its integration cycle arise from the non-critical M-theory spectrum and resolvent, providing a microscopic spectral realization of these completions. The correspondence fixes the nonconstant BPS sector and the cubic local contribution, while the remaining polynomial ambiguity and the modulus-independent constant-map sector require separate normalization. We explain why the single primitive spinless multiplet of the resolved conifold makes this identification possible, and discuss what additional charge- and spin-dependent microscopic data would be needed for an extension to more general local Calabi--Yau geometries.
发表机构
- Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京国际数学研究中心）
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