Gauge anomaly with vector and axial-vector fields in six dimensional curved space

TL;DR

This paper derives the gauge anomaly for fermions coupled to non-Abelian vector and axial-vector fields in six-dimensional curved space, highlighting the tensorial form and conditions under which certain terms vanish.

Contribution

It presents a tensorial expression for gauge anomalies in six-dimensional curved space involving non-Abelian vector and axial-vector fields, extending previous anomaly analyses.

Findings

Anomaly expressed in tensorial form for six-dimensional curved space.

Anomaly includes terms similar to chiral U(1) anomaly.

Commutator terms vanish when axial-vector field is Abelian.

Abstract

Imposing the conservation equation of the vector current for a fermion of spin $\frac{1}{2}$ at the quantum level, a gauge anomaly for the fermion coupling with non-Abelian vector and axial--vector fields in six--dimensional curved space is expressed in tensorial form. The anomaly consists of terms that resemble the chiral U(1) anomaly and the commutator terms that disappear if the axial--vector field is Abelian.