Direct construction of the effective action of chiral gauge fermions in the anomalous sector

TL;DR

This paper presents a new covariant method to directly construct the chiral invariant part of the effective action for chiral gauge fermions, overcoming previous obstructions caused by anomalies.

Contribution

It introduces a formulation that allows direct construction of the effective action's invariant part within a covariant framework, using an adapted Chan's approach in the derivative expansion.

Findings

Explicit expressions for the effective action up to four derivatives in 2D and 4D.

Leading order results in 2D and 4D, next-to-leading order in 2D.

A novel covariant formalism for chiral gauge theories.

Abstract

The anomaly implies an obstruction to a fully chiral covariant calculation of the effective action in the abnormal parity sector of chiral theories. The standard approach then is to reconstruct the anomalous effective action from its covariant current. In this work we use a recently introduced formulation which allows to directly construct the non trivial chiral invariant part of the effective action within a fully covariant formalism. To this end we develop an appropriate version of Chan's approach to carry out the calculation within the derivative expansion. The result to four derivatives, i.e., to leading order in two and four dimensions and next-to-leading order in two dimensions, is explicitly worked out. Fairly compact expressions are found for these terms.