Pauli-Villars' regularization of ghosts in path-integral string formulation

I consider Pauli-Villars’ regulators for the ghosts in the path-integral string formulation and show how they preserve conformal invariance. I calculate the regulator contributions to the effective action and to the central charge and demonstrate the consistency of the mean-field quantization of the Nambu-Goto string in $2<d\le 26$. The higher-derivative corrections to the Liouville action are briefly considered for the Pauli-Villars and proper-time regularizations.