  Explicit exact formulas are presented, for the leading order term in a strict
chiral covariant derivative expansion, for the abnormal parity component of the
effective action of two- and four-dimensional Dirac fermions in presence of
scalar, pseudo-scalar, vector and axial vector background fields. The formulas
hold for completely general internal symmetry groups and general
configurations. In particular the scalar and pseudo-scalar fields need not be
on the chiral circle.
