2020/12/02 by Wee Chaimanowong, Chaimanowong, Wee
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2012.01383
openalex publication_date 2020/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kontsevich-Soibelman (2017) reformulated Eynard-Orantin topological recursion (2007) in terms of Airy structure which provides some geometrical insights into the relationship between the moduli space of curves and topological recursion. In this work, we investigate the analytical approach to this relationship using the Seiberg-Witten family of curves as the main example. In particular, we are going to show that the formula computing the Hitchin systems' Special Kahler's prepotential from the genus zero part of topological recursion as obtained by Baraglia-Huang (2017) can be generalized for a more general family of curves embedded inside a foliated symplectic surface, including the Seiberg-Witten family. Consequently, we obtain a similar formula relating the Seiberg-Witten prepotential to the genus zero part of topological recursion on a Seiberg-Witten curve.