Abstract We provide a rigorous lattice approximation of conformal field theories given in terms fermions 1+1-dimensions, focussing on free fermion models and Wess–Zumino–Witten models. To this end, we utilize recently introduced operator-algebraic framework for Wilson–Kadanoff renormalization. In setting, prove the convergence Virasoro generators by Koo–Saleur formula. From this, deduce approxi...