Derivative expansion for the effective action of chiral gauge fermions. The abnormal parity component

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 the 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. Received: 31 January 2001 / Published online: 12 April 2001