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

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