The quadratic WDVV solution $E_8(a_1)$

TL;DR

This paper explicitly computes the quadratic solution to the WDVV equations associated with the $E_8(a_1)$ conjugacy class using classical W-algebra techniques.

Contribution

It provides the first explicit quadratic WDVV solution for the $E_8(a_1)$ class, advancing understanding of Frobenius manifolds related to exceptional Lie groups.

Findings

Explicit quadratic WDVV solution for $E_8(a_1)$

Methodology using classical W-algebra

Contributes to classification of Frobenius manifolds

Abstract

We calculate explicitly the quadratic solution to the WDVV equations corresponds to the quasi-Coxeter conjugacy class $E_8(a_1)$ using the associated classical $W$-algebra.