Logarithmic deformations of the rational superpotential/Landau-Ginzburg construction of solutions of the WDVV equations

TL;DR

This paper introduces logarithmic deformations to the superpotential in Landau-Ginzburg models, leading to new quadratic deformations of WDVV solutions, including polynomial solutions with pseudo-quasi-homogeneity.

Contribution

It presents a novel method of deforming WDVV solutions via logarithmic terms in the superpotential, expanding the class of known solutions.

Findings

Deformation solutions satisfy pseudo-quasi-homogeneity conditions

Includes polynomial solutions as special cases

Provides a new class of solutions to WDVV equations

Abstract

The superpotential in the Landau-Ginzburg construction of solutions to the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations is modified to include logarithmic terms. This results in deformations - quadratic in the deformation parameters - of the normal prepotential solution of the WDVV equations. Such solution satisfy various pseudo-quasi-homogeneity conditions, on assigning a notional weight to the deformation parameters. This construction includes, as a special case, deformations which are polynomial in the flat coordinates, resulting in a new class of polynomial solutions of the WDVV equations.