发表机构
New York University（纽约大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对物理学中应用的带无限分歧轨迹的谱曲线，严格定义拓扑递归并证明其性质，填补数学文献空白，还发现不同谱曲线可产生相同量子曲线的新现象。
AI 中文摘要
近来物理学文献中已有少量但不断增多的论文将Eynard-Orantin拓扑递归程序应用于具有无限基数分歧轨迹的谱曲线。然而数学文献中存在相应空白：尚未严格验证所得无穷级数是否收敛，以及所得关联函数是否具备拓扑递归所需的全部性质。本研究旨在填补该空白，通过定义适用于前述物理学应用的、范围足够广泛的谱曲线上的拓扑递归，并严格证明该定义具备人们直观预期的性质。作为副产品，还发现了涉及量子曲线的有趣巧合：两条不同的谱曲线会产生相同的量子曲线，这种情形此前在文献中尚未出现过。
英文摘要
Recently in the physics literature there have been a small, but growing, number of papers that have applied the Eynard-Orantin topological recursion procedure to spectral curves with ramification loci of infinite cardinality. However, there is a corresponding gap in the mathematics literature; indeed, it has not been checked rigorously whether the resulting infinite sums converge, or whether the resulting correlators have all the desired properties of the topological recursion. The present work aims to bridge this gap by defining topological recursion on a suitably broad class of spectral curves to cover the aforementioned physics applications and to rigorously prove that this definition has the properties one would intuitively expect. As a by-product, some interesting coincidences involving quantum curves are discovered, where two different spectral curves yield the same quantum curve, a situation that has, hitherto, not appeared in the literature.
Comments38 pages plus appendices
