  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.
