发表机构
ETH Zürich（苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Calabi-Yau五重流形的等变Gromov-Witten不变量，提出M2-膜的模解释，推导相关Hodge积分闭式公式，证明猜想在等变参数两极限下成立，关联了Gromov-Witten理论与Donaldson-Thomas理论。
AI 中文摘要
在正次数下，Calabi-Yau五重流形的等变Gromov-Witten不变量被期望可通过M2-膜来解释，而我们猜想常值映射由对应的超引力指数支配。我们通过提出一种支撑在若干交于n重点的光滑曲线上的M2-膜的模解释，使前一期望变得明确。结合这两种图景，我们得到Gromov-Witten不变量的猜想公式，并将其转化为带点与不带点的五次Hodge积分的闭式公式。我们证明这些猜想蕴含了一次局部曲线的K-理论Gromov-Witten/配对对应，并将常值映射的生成级数与点的Donaldson-Thomas理论关联起来。我们还在等变参数的两个极限下证明了这些猜想，在此过程中得到了某些三重Hodge积分的新闭式公式。
英文摘要
In positive degree, equivariant Gromov-Witten invariants of Calabi-Yau fivefolds are expected to admit an interpretation in terms of M2-branes, while we conjecture that constant maps are governed by the corresponding supergravity index. We make the first expectation precise by proposing a modular interpretation of M2-branes supported on several smooth curves meeting at an $n$-fold point. Together, the two pictures yield conjectural formulas for the Gromov-Witten invariants, which we translate into closed formulas for pointed and unpointed quintuple Hodge integrals. We show that these conjectures imply a K-theoretic Gromov-Witten/Pairs correspondence for local curves in degree one and link the generating series of constant maps to Donaldson-Thomas theory of points. We also prove the conjectures in two limits of the equivariant parameters. Along the way, we obtain new closed formulas for certain triple Hodge integrals.
Comments47 pages, 3 figures. Comments welcome
