Duality for Jacobi group orbit spaces and elliptic solutions of the WDVV equations

Abstract

From any given Frobenius manifold one may construct a so-called dual structure which, while not satisfying the full axioms of a Frobenius manifold, shares many of its essential features, such as the existence of a prepotential satisfying the WDVV equations of associativity. Jacobi group orbit spaces naturally carry the structures of a Frobenius manifold and hence there exists a dual prepotential. In this paper this dual prepotential is constructed and expressed in terms of the elliptic polylogarithm function of Beilinson and Levin.

References in corpus (4)

• Solutions of WDVV equations in Seiberg-Witten theory from root systems
• Frobenius Manifolds: Natural submanifolds and induced bi-Hamiltonian structures
• Seiberg-Witten theory for a non-trivial compactification from five to four dimensions
• Locus configurations and $\vee$-systems

Cited by in corpus (4)

• Weyl groups and Elliptic Solutions of the WDVV equations
• Polynomial Modular Frobenius Manifolds
• Loewner equations, Hirota equations and reductions of universal Whitham hierarchy
• Modular Frobenius manifolds and their invariant flows