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

TL;DR

This paper derives explicit formulas up to fourth order for the normal parity part of the effective action of Dirac fermions in even dimensions, considering general bosonic backgrounds without symmetry constraints.

Contribution

It provides the first exact, covariant derivative expansion formulas for the normal parity component of the effective action in a broad, symmetry-independent setting.

Findings

Explicit formulas up to fourth order in derivatives are obtained.

The results apply to general scalar, pseudo-scalar, vector, and axial vector backgrounds.

No assumptions on internal symmetry groups or chiral circle constraints are made.

Abstract

Explicit exact formulas are presented, up to fourth order in a strict chiral covariant derivative expansion, for the normal parity component of the Euclidean effective action of even-dimensional Dirac fermions. The bosonic background fields considered are scalar, pseudo-scalar, vector and axial vector. No assumptions are made on the internal symmetry group and, in particular, the scalar and pseudo-scalar fields need not be on the chiral circle.