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

TL;DR

This paper provides explicit formulas for the leading order abnormal parity component of the effective action of chiral fermions in various dimensions, accommodating general background fields and symmetries.

Contribution

It introduces exact, general formulas for the abnormal parity part of the effective action in chiral gauge theories, extending previous results to broader configurations.

Findings

Explicit formulas for 2D and 4D cases

Applicable to general symmetry groups and configurations

No restriction to chiral circle for scalar fields

Abstract

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.