论文标题
NAHM总和，Quiver a-Polynomials和拓扑递归
Nahm sums, quiver A-polynomials and topological recursion
论文作者
论文摘要
我们考虑了具有NAHM总和的结构或Quivers的动机生成系列的大型$ q $ series。首先，我们对与此类$ Q $ series相关的经典和量子A-聚合物进行系统分析和分类。这些量子Quiver a-多项式编码上述序列满足的递归关系，而经典的A-聚合物编码了这些系列的渐近扩展。其次，我们假设这些系列及其量子颤动a-多项式可以通过拓扑递归重建。零属有大量有趣的箭量a-多项式，对于其中的许多人，我们通过显式计算确认上述猜想。鉴于最近发现的二元性，为了适当选择Quivers，这些结果在拓扑弦理论，结理论，晶格路径的计数和相关主题中具有直接的解释。特别是，它表征了这些系统的各种数量，例如动机唐纳森 - 托马斯不变，各种结的不变性等，都具有与拓扑递归兼容的结构，并且可以通过其手段重建。
We consider a large class of $q$-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such $q$-series. These quantum quiver A-polynomials encode recursion relations satisfied by the above series, while classical A-polynomials encode asymptotic expansion of those series. Second, we postulate that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them we confirm the above conjecture by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means.
