Covariance of WDVV equations

TL;DR

This paper investigates the covariance properties of the WDVV equations in various physical models, showing that while variables and prepotentials transform non-trivially, the period matrix remains invariant, revealing underlying symmetries.

Contribution

It demonstrates the covariant nature of (generalized) WDVV equations under non-linear transformations in topological and Seiberg-Witten models, highlighting invariance of the period matrix.

Findings

Period matrix remains invariant under transformations.

Prepotentials and variables transform non-trivially.

Covariance extends to 2d, 4d, and 5d models.

Abstract

The (generalized) WDVV equations for the prepotentials in $2d$ topological and $4,5d$ Seiberg-Witten models are covariant with respect to non-linear transformations, described in terms of solutions of associated linear problem. Both time-variables and the prepotential change non-trivially, but period matrix (prepotential's second derivatives) remains intact.