"Real doubles" of Hurwitz Frobenius manifolds

TL;DR

This paper introduces new Frobenius structures on Hurwitz spaces viewed as real manifolds, doubling the coordinate system and utilizing branch points and their conjugates to solve WDVV equations.

Contribution

It presents novel Frobenius structures on Hurwitz spaces as real manifolds, expanding the coordinate framework and deriving solutions to WDVV equations.

Findings

New Frobenius structures on Hurwitz spaces as real manifolds

Explicit solutions to WDVV equations and G-functions

Use of branch points and conjugates as canonical coordinates

Abstract

New Frobenius structures on Hurwitz spaces are found. A Hurwitz space is considered as a real manifold; therefore the number of coordinates is twice as large as the number of coordinates on Hurwitzs Frobenius manifolds of Dubrovin. Simple branch points of a ramified covering and their complex conjugates play the role of canonical coordinates on the constructed Frobenius manifolds. Corresponding solutions to WDVV equations and G-functions are obtained.