Open Hurwitz Flat F Manifolds

Abstract

In this paper, we derive Open WDVV equations starting from any Hurwitz Dubrovin Frobenius manifold. The WDVV equations plays a crucial role in the structure of Frobenius manifolds, quantum cohomology, and integrable systems. Extending these ideas, Open WDVV equations provide a framework to incorporate boundary conditions, making them fundamental in Open Gromov-Witten theory. Using Dubrovin’s construction of Landau-Ginzburg superpotentials associated with Hurwitz spaces, we demonstrate that their primitives satisfy Open WDVV equations. Our approach provides an efficient method for computing Open WDVV equations associated with any Hurwitz Dubrovin Frobenius manifold.

Keywords: Open Gromov Witten theory, Dubrovin Frobenius manifolds, Hurwitz spaces.