New conformal field theory from $mathcal{N}=(0,2)$ Landau-Ginzburg model

By studying the infra-red fixed point of an $mathcal{N}=(0,2)$ Landau-Ginzburg model, we find an example of modular invariant partition function beyond the ADE classification. This stems from the fact that a part of the left-moving sector is a new conformal field theory which is a variant of the parafermion model.