Path-integral derivation of gauge and gravitational chiral anomalies in theories with vector and axial-vector couplings in arbitrary even dimensions

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Abstract
The anomalies associated with general linear transformations of fermions coupled to external vector and axial-vector fields in curved spaces of arbitrary even dimensions are derived within the path-integral framework. The anomalies are due to the noninvariance of the fermionic functional measure under these transformations. The anomalies satisfy the Wess-Zumino consistency conditions. This implies that the choice of the fermionic functional measure is the correct one. Special cases of the general formula obtained agree with all previous results.

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