  An essential assumption in the Vafa and Witten's theorem on P and CT
realization in vector-like theories concerns the existence of a free energy
density in Euclidean space in the presence of any external hermitian symmetry
breaking source. We show how this requires the previous assumption that the
symmetry is realized in the vacuum. Even if Vafa and Witten's conjecture is
plausible, actually a theorem is still lacking.
