广义环 Calabi-Yau 三维流形的 BPS 不变量
BPS Invariants for Generalized Toric Calabi-Yau Threefolds
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中文总结 AI 辅助
该研究将拓扑顶点技术应用于含多5-膜终止于同一7-膜的膜网对偶Calabi-Yau三维流形，明确拓扑弦配分函数在Hanany-Witten转变和flop变换下的变换，提出高效计算任意次数和亏格Gopakumar-Vafa不变量的技术，并首次得到dP₄的高次不变量。
中文摘要 AI 辅助
我们将拓扑顶点技术应用于对偶于膜网的 Calabi-Yau 三维流形，其中多个 5-膜可终止于同一 7-膜上。在此背景下，我们确定了拓扑弦配分函数在 Hanany-Witten 转变和 flop 变换下的变换方式，这使我们能够追踪此类转变下的曲线及相关不变量。平行外部膜的贡献形成一个对 5d SCFT 不可见的普适部分；移除该部分后，不变量可在构建同一理论的不同几何之间转移。这为计算任意次数和亏格的 Gopakumar-Vafa 不变量提供了一种高效技术。我们以局部 Hirzebruch 曲面和 del Pezzo 曲面（包括 dP₄）为例进行说明，首次获得了其高次不变量。
英文摘要
We apply topological vertex techniques to Calabi-Yau threefolds dual to brane webs where several 5-branes can end on the same 7-brane. In this context, we determine how topological string partition functions transform under Hanany-Witten transitions and flops, which allows us to track curves and the associated invariants under such transitions. The contributions of parallel external branes form a universal sector invisible to the 5d SCFT; once it is removed, invariants can be transported between different geometries engineering the same theory. This yields an efficient technique to compute Gopakumar-Vafa invariants at any degree and genus. We illustrate this with local Hirzebruch and del Pezzo surfaces, including $dP_4$, whose invariants we obtain at high degree for the first time.
