Seiberg-Witten Theory and Topological Recursion
AffiliationSchool of Mathematics and Statistics
Document TypePhD thesis
Access StatusOpen Access
© 2020 Wee Chaimanowong
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. Finally, we investigate the connection between Seiberg-Witten theory and Frobenius manifolds which potentially enable the generalization of the current result to include the higher genus parts of topological recursion in the future.
KeywordsSeiberg-Witten theory; Topological Recursion; Airy Structures; Frobenius Manifolds; Prepotential; Differential Geometry; Symplectic Geometry; Mathematical Physics
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