On exact solution of topological CFT models based on Kazama-Suzuki cosets

TL;DR

This paper computes flat coordinates on Frobenius manifolds related to Gepner ${SU}(3)_k$ chiral rings, crucial for exact solutions in topological CFT and 2D Liouville gravity, with a focus on the special case k=3.

Contribution

It provides explicit forms of flat coordinates for the deformation space of Gepner ${SU}(3)_k$ chiral rings, especially addressing the complexities introduced by marginal perturbations at k=3.

Findings

Explicit flat coordinates for k=3 case.

Analysis of marginal perturbations in topological CFT.

Enhanced understanding of deformation spaces in Frobenius manifolds.

Abstract

We compute the flat coordinates on the Frobenius manifolds arising on the deformation space of Gepner $\hat{SU}(3)_k$ chiral rings. The explicit form of the flat coordinates is important for exact solutions of models of topological CFT and 2d Liouville gravity. We describe the case k=3, which is of particular interest because apart from the relevant chiral fields it contains a marginal one. Whereas marginal perturbations are relevant in different contexts, their analysis requires additional care compared to the relevant perturbations.