Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-08-23 DOI:10.1016/j.geomphys.2024.105306

Vincent Bouchard , Reinier Kramer , Quinten Weller

引用次数: 0

Abstract

Given a spectral curve with exponential singularities (which we call a “transalgebraic spectral curve”), we extend the definition of topological recursion to include contributions from the exponential singularities in a way that is compatible with limits of sequences of spectral curves. This allows us to prove the topological recursion/quantum curve correspondence for a large class of transalgebraic spectral curves. As an application, we find that Atlantes Hurwitz numbers, which were previously thought to fall outside the scope of topological recursion, satisfy (our extended version of) topological recursion, and we construct the corresponding quantum curve directly from topological recursion.

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跨代数谱曲线上的拓扑递归和阿特兰迪斯-赫尔维茨数

给定一条具有指数奇异点的光谱曲线（我们称之为 "跨代数光谱曲线"），我们扩展拓扑递推的定义，以包括指数奇异点的贡献，这种方式与光谱曲线序列的极限相容。这样，我们就能证明一大类跨代数谱曲线的拓扑递归/量子曲线对应关系。作为一个应用，我们发现以前被认为不属于拓扑递归范围的亚特兰蒂斯胡尔维兹数满足（我们扩展版本的）拓扑递归，并且我们直接从拓扑递归构造了相应的量子曲线。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

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