发表机构
Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学理论交叉研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用恢复理论研究拓扑弦非微扰贡献的模性质，证明斯托克斯常数在轨道上相同，并识别全局斯托克斯变换为Kontsevich-Soibelman墙交叉不变量。
AI 中文摘要
拓扑弦自由能具有丰富的非微扰贡献，这些贡献由D-膜电荷向量标记，且相关的斯托克斯常数被推测与BPS或DT不变量（即D-膜重数）一致。本文通过研究非微扰贡献的模性质，为该猜想提供了额外证据。我们利用恢复理论论证，非微扰贡献形成由稳定室内的奇点诱导的局部单值群的轨道，且相关的斯托克斯常数在轨道上必须相同。在某些例子中，这可以生成无限多个斯托克斯常数，再现整个BPS谱。此外，遵循[DK26]，我们还证明了非全纯配分函数的斯托克斯变换生成元满足Kontsevich-Soibelman李代数的李括号，从而可以将全局斯托克斯变换识别为Kontsevich-Soibelman墙交叉不变量。
英文摘要
Topological string free energy has a rich collection of non-perturbative contributions which are labeled by D-brane charge vectors, and the associated Stokes constants are conjectured to coincide with BPS or DT invariants, i.e. D-brane multiplicities. In this paper, we provide additional evidence to this conjecture by studying modular properties of non-perturbative contributions. We argue using resurgence theory that non-perturbative contributions form orbits of local monodromy group induced by singular points inside a stability chamber, and that the associated Stokes constants must be the same across the orbits. In some examples, this allows generation of infinitely many Stokes constants, which reproduce the entire BPS spectrum. In addition, following [DK26], we also show that generators of Stokes transformations of non-holomorphic partition function satisfy Lie brackets of the Kontsevich-Soibelman Lie algebra, making it possible to identify the global Stokes transformation with the Kontsevich-Soibelman wall-crossing invariant.
Comments44 pages, 15 figures
