Flat structures on the deformations of Gepner chiral rings

TL;DR

This paper introduces a straightforward method to compute flat coordinates and primitive forms on Frobenius manifolds related to deformations of Jacobi rings, aiding in solving topological conformal field theories.

Contribution

It presents a new linear approach based on integral representations and Saito cohomology for computing flat structures in deformed Gepner chiral rings.

Findings

Simplified computation of flat coordinates and primitive forms.

Application to deformed Gepner chiral rings.

Facilitates exact solutions in topological conformal field theories.

Abstract

We propose a simple method for the computation of the flat coordinates and Saito primitive forms on Frobenius manifolds of the deformations of Jacobi rings associated with isolated singularities. The method is based on using a conjecture about integral representations for the flat coordinates and on the Saito cohomology theory. This reduces the computation to a simple linear problem. We consider the case of the deformed Gepner chiral rings. The knowledge of the flat structures of Frobenius manifolds can be used for exact solution of the models of the topological conformal field theories corresponding to these chiral rings.