标题： GW/DT 不变量和从拓扑递归得到的条带的5D BPS 指数 显示英文标题

标题： GW/DT invariants and 5D BPS indices for strips from topological recursion

摘要： 拓扑弦理论的划分函数产生格罗莫夫-威滕不变量、唐纳森-托马斯不变量和5D BPS指标。 通过连接拓扑递归和环面卡拉比-丘3流形的拓扑弦理论的重塑猜想，对条带几何的子类进行了更直接的联系研究。 在这一过程中，应用了拓扑递归理论的新发展，作为其对对数拓扑递归（Log-TR）和普遍$x$--$y$对偶性的扩展。 通过这些技术，本文的主要结果是对一般条带几何的拓扑递归的所有自由能的直接推导。 在分析自由能的表达式时，我们对$x$--$y$对偶性在拓扑弦理论中的意义和影响，以及它与GW和DT不变量及5D BPS指标之间的相互联系提供了一些见解。 显示英文摘要

摘要： Topological string theory partition function gives rise to Gromov-Witten invariants, Donaldson-Thomas invariants and 5D BPS indices. Via the remodeling conjecture connecting Topological Recursion and topological string theory for toric Calabi-Yau 3-folds, a more direct connection is studied for the subclass of strip geometries. In doing so, new developments in the theory of topological recursion are applied as its extension to Logarithmic Topological Recursion (Log-TR) and the universal $x$--$y$ duality. Through these techniques, our main result in this paper is a direct derivation of all free energies from topological recursion for general strip geometries. In analyzing the expression of free energy, we shed some light on the meaning and the influence of the $x$--$y$ duality in topological string theory and its interconnection to GW and DT invariants as well as the 5D BPS index.