Fermionic and parafermionic CFTs with su(2) and su(3) symmetry

We investigate two-dimensional conformal field theories (CFTs) with affine su(2) and su(3) algebra symmetry. Their bosonic modular-invariant partition functions have been fully classified based on the ADE classification. In this work, we extend the classification to include fermionic and parafermionic CFTs with the same affine symmetries, utilizing techniques of fermionization and parafermionization. We find that the fermionic and parafermionic su(2) models are related to non-simply laced Dynkin diagrams.