Flat structures on Frobenius Manifolds in the case of irrelevant deformations

TL;DR

This paper computes flat coordinates and primitive forms on Frobenius manifolds associated with deformations of Gepner chiral rings, verifying a conjecture using integral representations, especially in cases involving irrelevant deformations.

Contribution

It applies a recent conjecture to explicitly compute flat structures on Frobenius manifolds related to isolated singularities, including cases with irrelevant deformations.

Findings

Confirmed the conjecture by matching integral representation results with direct computations.

Explicitly computed flat coordinates and primitive forms for the Gepner $ ext{SU}(3)_4$ case.

Analyzed the structure of Frobenius manifolds with irrelevant deformations.

Abstract

In this paper we use the recently suggested conjecture about the integral representation for the flat coordinates on Frobenius manifolds, connected with the isolated singularities, to compute the flat coordinates and Saito primitive form on the space of the deformations of Gepner chiral ring $\widehat{SU}(3)_4$. We verify this conjecture comparing the expressions for the flat coordinates obtained from the conjecture with the one found by direct computation. The considered case is of a particular interest since together with the relevant and marginal deformations it has one irrelevant deformation.