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

TL;DR

This paper constructs a dual prepotential for Jacobi group orbit spaces, expressed via elliptic polylogarithms, revealing new insights into solutions of the WDVV equations related to Frobenius manifolds.

Contribution

It introduces a novel dual prepotential for Jacobi group orbit spaces using elliptic polylogarithms, expanding the understanding of Frobenius manifold structures.

Findings

Explicit dual prepotential expressed in elliptic polylogarithms

Connections between Jacobi orbit spaces and elliptic solutions of WDVV equations

Enhanced understanding of Frobenius manifold dual structures

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.