Flat structures on the deformations of Gepner chiral rings

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.