Solutions of $BC_{n}$ Type of WDVV Equations

TL;DR

This paper constructs a family of solutions to the WDVV equations using the $BC_{n}$ root system and applies them to develop ${ m extbf{N}}=4$ supersymmetric mechanical systems, expanding the understanding of these mathematical structures.

Contribution

It introduces a new family of solutions to the WDVV equations based on the $BC_{n}$ root system with multiple parameters, and demonstrates their application in supersymmetric mechanics.

Findings

Defined solutions in terms of $BC_{n}$ root system and parameters

Connected solutions to ${ m extbf{N}}=4$ supersymmetric systems

Extended the class of known WDVV solutions

Abstract

We give a family of solutions of Witten-Dijkgraaf-Verlinde-Verlinde equations in $n$-dimensional space. It is defined in terms of $BC_{n}$ root system and $n+2$ independent multiplicity parameters. We also apply these solutions to define some ${\mathcal N}=4$ supersymmetric mechanical systems.